First of all, you must speak to Zeus. Head right until you find a white house (Check the picture above) and go inside to find the first boss of the game, the Bull. It's quite simple to defeat him, just wait for him to move towards you and attack. After 4 attacks, you'll slay it and the entrance to Zeus Temple will open, so head there.
At the temple, Zeus says he heard about your story thanks to Aphrodite and that he will speak to the other gods to bless you with their powers. Now go back one screen left and enter the house heading for Attica.
Reaching Attica, head right, go down the stairs, then head right again to find the entrance to Athens (Check the picture above). Enter the city, head right until the end of the city and open the door that takes to Athena's temple. Speak to her to receive the Shield of Athena (It reflects the attacks of certain enemies and you'll use it against the next boss). Head back to the entrance of Athens, go left, then down the stairs, then left again to find the Lamia.
To defeat the Lamia, wait until she approaches, defending yourself from her arrows, then jump over an arrow and hit her when she's close enough, then run away. Doing this 6 times is enough to beat the Lamia. After your victory, a door will open and you'll find a child that had been kidnapped by the Lamia. Speak to the child, head back right one screen and speak to the child's mother at the house shown on the pic above to get the Staff of Fennel.
Now that you possess the Staff of Fennel, you must head to Argolis to get the Fire of Prometheus, allowing you to cast fire with the Staff of Fennel. To reach Argolis, head back all the way to Arcadia, then head left 2 screens and enter the door shown at the pic above to find another door. Open it also, head left all the way to reach Argolis.
Head right and you'll find 2 entrances at the cave, but use the right entrance and head until the place shown on the picture above, then enter the door. You'll be inside Hermes' temple, and one of the servants will say that Zeus has called you. That means you should return to Zeus' temple, but before doing that, fall down the pit to the left of the entrance of Hermes' temple to find the Salamander's Nest. Collect 50 Olives here to buy Ambrosia at the center room and pick 20 Salamander Skins too (You'll use those later). Now exit through the last door to the right and head back to Zeus' temple, at Arcadia.
At Zeus' temple, you'll meet Hermes and receive the Sandals of Hermes from him (D'oh). With it, you can jump higher and walk on the ceiling (Jump and hold jump button to walk on the ceiling). Head back to Argolis and this time follow the left entrance of the cave. Just keep moving until you find the Lion of Nemea. To defeat it, wait for him (as usual) and attack withe the Staff of Fennel 3 times. Enter the door that appears after defeating him, then speak to Prometheus to learn to use the Fire of Prometheus (Press Up + Attack button while equipped with the Staff of Fennel to use it). Now you must head to Peloponnesus, so head back to Arcadia, continue right until the end and enter the door.
At Peloponnesus, you must find Apollo's temple. Head right until you find an entrance at the end of the map, then enter the first door to the right, then the second door to the left (Check the temple entrance on the pic above). Apollo will hand you the Apollo's Harp (So Egocentric, those Greek Gods, uh? :P), which allows you to summon the Pegasus (Check the items section for more info).
Still at Peloponnesus, you must find the Sword. From Apollo's temple, enter the first door to the right twice, follow the path jumping on the trees, crossing through the green bushes until you reach a red bush (Check the picture above), then burn it with the Fire of Prometheus and keep going left to reach the Hydra. To defeat the Hydra, notice the bubbles (that's where the Hydra is coming out from) and wait from a certain distance, then strike it on the head 8 times. A platform will show up after the bridge; Jump on it, enter the door and speak to the faerie to get the Sword.
Head back to the forest maze and enter the third door to the left, heading to the place shown on the picture above. Strike that exact spot to get an Ambrosia, then keep going left to meet the Cyclops. To defeat him, you must hit his head with the Sword 4 times. After that, enter the door to the left to reach Laconia.
At Laconia, you must get the Trojan Pitcher first. Head right until you find the spot shown on the upper part of the picture above and hit the base of the pillar. The Trojan will fall from the top of the pillar, and now you should head to Poseidon's temple.
Check the lower part of the picture above and hit the pillar to open a hole in the ground. Fall in it, then enter the door to reach a pitch dark room. Equip the Staff of Fennel and use the Fire of Prometheus to light the room. Enter the door a bit ahead of you to reach Poseidon's temple. Buy the Ocarina for 60 Olives, then go down the closest stairs to you and head all the way right, entering the lower door. Use the Fire of Prometheus at another dark room and fight a stronger Cyclops a bit ahead (Dies after 6 hits). You'll get an Ambrosia for that, then head to the back door and fill your Trojan Pitcher on the fountain. Head back to the upper floor and move right until you reach the sea and use the Ocarina to summon the Dolphin. Hop on it and head right until you reach an island.
At the island, you'll find a boss: Siren. To defeat her, use Apollo's Harp to avoid being hypnotized and hit her 3 times with the Sword. A door will show up and you'll fall in a dark room. Use the Fire of Prometheus to light the room and head right to find the Graeae. The Graeae is composed of 3 mages that appear and dissapear randomly while attacking. You must wait for them to appear and strike each of them 3 times with the Sword. You'll win the Eye of Graeae, which allows you to find invisible doors. Now you must find the first Nymph, and for that you must go back to Argolis. Enter the cave to the left and use the Eye of Graeae on the beginning of the cave (Check the picture above) to reveal a door. Enter it and head left, then open the upper door to find the first Nymph and receive the first Token of Love that serves as a proof of courage. Now head back to Attica and speak to Keleos.
Back at Attica, go to Athens, enter the mansion shown on picture above and speak to Keleos to receive the Key. Head to the entrance of Athens, then head right, where Gaea blocks the way to Phthia, then use the Ocarina to wake him up. Use the same strategy from the Cyclops to defeat Gaea, then proceed to Phthia.
At Phthia, go left all the way to find Hephaestus' temple and buy a Divine Sword for 70 Olives (Best weapon of the game, you can shoot rays with it by pressing Up + Attack button; It costs HP, though). After that, go back to the place shown on the picture above, go inside and get another Ambrosia. Head back to Phthia's entrance, but head right this time untl you find stairs. Go up, turn right and meet the Centaur. You're not forced to fight him, but if you want to, watch out for his arrows and jump when you're close enough to strike him.
After the Centaur, there's a waterfall with 2 secret entrances (You can see both on the picture above). Go inside the upper secret entrance and move a few steps before the door to the right, then use the Eye of Graeae to find another entrance. Go through it to find another Nymph that will give you the second Token of Love.
This is an optional part (You can skip this paragraph), but it is HIGHLY recommended. After getting the second Token of Love, enter the door to the right and you'll reach Hesperides' Garden. Keep going right until you find Ladon (Similar to the Hydra, but it flies). Blast it with the Divine Sword's rays 10 times and you'll receive a golden apple (Restores ALL your HP and halves the damage inflicted by enemies).
After getting the second Token of Love, you must go to Crete. Head back the way you came and use the harp at the monolith of sun (Check the picture above). The Pegasus will show up and take you to Laconia. Head right crossing Siren's island and right before entering Crete, you'll fight Talos at Crete's entrance. Crouch while waiting for him to get closer and attack him 4 times to win. Continue to enter Crete's labyrinth.
At Crete you must go first to Ares' temple to buy a Power Bracelet. Enter the door to the left of Crete's entrance, head right to another screen and enter the first door. Go through the yellow room to reach Ares' temple. Buy a Power Bracelet for 80 Olives, but MAKE SURE YOU HAVE THE MONEY BEFORE BUYING. If you do not have enough money, you'll lose the Sandals of Hermes (the Sandals can obtained again from Hermes if you visit his temple and Zeus' temple again). The Bracelet of Power doubles your damage and the Divine Sword's ray won't take HP anymore.
Now you must buy the Salamander Shield. Get 80 Olives again and head back to the door that takes you to an area with golden walls, enter the door to the right, head right, enter the first door on the next screen, head right, then enter the first door on the next screen again to find an area with red walls (Check the picture above). Cross the door to the right to meet Circe. Give her 20 Salamander Skins and 80 Olives to get the Salamander Shield. Your next step is to find and defeat the Minotaur.
Head back to the red walls' area, enter the door to the right, then the second door to the right (You can check the first door here if you need Nectar), then you'll reach an energy barrier that will open because you have the second Token of Love. After the barrier, you must fight the Minotaur. Use the Divine Sword's special attack 8 times on his head to defeat him (If you don't have the Power Bracelet, you must hit him 16 times). Enter the door that appears after your victory to meet another Nymph and get the third Token of Love. This Token allows you to enter Tartarus (No, not the server where you shrine, silly :P), but first you must head to Phrygia.
To reach Phrygia you must summon the Dolphin at the coast nearby the place where you fought the Lamia at Attica (Check the picture above) and cross the sea. Right at the entrance, you'll fight a Dark Pegasus. Defeat it with 2 hits (I'm assuming you have the Bracelet of Power) and enter Phrygia. Head right and enter the last door to fight the Giant Snake. Block the fire balls with your shield, then use the Divine Sword's rays to defeat it. Go up the stairs the Giant Snake protected and open the door. Follow the stairs to the next floor, then head left following another set of stairs until you find a door.
Inside you'll find another Giant Snake, defeat it and go down 2 sets of stairs to the lower floor and enter the door. Go up the stairs and head right, jumping over the platforms (Check picture above), go down the stairs and enter another door. Go up the stairs and enter the door to get the last Ambrosia. Head back through the stairs, defeat another Giant Snake, go down the stairs, enter the second door to the left, then go up the stairs all the way until you reach Artemis' palace. Speak to Artemis to receive the Moon Orb, which will help you on your final battle against Hades.
Now that you possess everything you need to defeat Hades, head to Tartarus. The entrance is located at the sea between Argolis and Crete (Check the picture above). Go inside and you'll fall in a room with 2 doors. Enter the doors in the following order to avoid fighting a boss: Left, Left, Right, Left. After going through you'll fight the Cerberus. You must destroy both heads (each of them will die with 4 Divine Sword hits, equipped with the Bracelet of Power), but after defeating the first head, you must quickly destroy the second or else the other head will regenerate. Try staying still and keep jumping using the Power of Argus when it runs on your direction. After this battle, enter the door that appears.
Watch out while moving on the branches; You can meet a servant of Aphrodite that heals your HP on the first room. Keep going to the right until you find 2 more doors and enter the left one, then head right by the ceiling with the Sandals of Hermes, then enter the last door to the right. At this new area of Tartarus, you'll use the Sandals of Hermes to move by the ceiling and cross the pit. After the pit, head right until you find 2 doors and enter the upper one. Continue until you reach a cave, then head right jumping over the platforms and enter the upper door. Head left crossing the bridge and enter the door. You'll fall between 2 doors, enter the left one and keep heading left to reach the last door and finally go inside Hades' Palace.
Head right and you'll meet a Lamia, but you're not forced to destroy it, so simply ignore it and continue right until you find some stairs. Go up, head left and check the door you pass by if you want (There's a man selling Nectar for 30 Olives inside), if not, go up another set of stairs.
Keep going to the right and jumping over the platforms, ignore the first stairs until you find another set of stairs. Go up and continue the path, then go down another stairs to find a room with your petrified lover. Equip the Moon Crystal and enter Hades' room.
To defeat Hades, use the Moon Crystal to see his shadow on the water and keep attacking him until he shows up (He'll have half of his HP by now). Keep attacking until you defeat him. After your victory, head back to the previous room and watch the ending. Congratulations!