Here's a simple walkthrough to help you find your way through the game.
You will start out at Cross Town High, just make your way right one screen then up one screen and you will reach Grotto Mall with out any incident. Go ahead and fight the random gang members if you feel up to it.
Buy anything you feel you need from Grotto Mall. If you have the cash, you should buy either Stone Hands or Dragon Feet, your choice. If you don't have the money you may want to fight until you do. These items will make the coming battles much easier.
In the next screen, Sticksville, you will notice you have two choices, up or right. Up is a dead end, there will be a boss fight later, but not until some other conditions are met, so continue to the right.
Alright, this will be your first boss battle. Here and in most upcoming boss battles, you must defeat a bunch of gang members before the boss will appear. Do this, then beat the crap out of Moose and continue upwards.
Here is the second mall, Waterfront Mall. Eat some food if you need some stamina. If you haven't done so yet, buy Stone Hands or Dragon Feet. Also in this mall is the first place you can buy healing items that you can take with you, so you may want to buy some stuff from Jones' Pharmacy if you think you'll need it. Continue to the right.
Here on Capitol Ave Bridge, you'll meet Roxy, she'll give you some information on Slick, Cyndi, and the brothers Benny and Clyde. As soon as she stops talking, go upwards, right before the bridge starts.
Under the Capitol Ave Bridge you'll meet the second boss(es), Benny and Clyde. These two are a good way to get money, so once you defeat them, feel free to come back and fight them over and over to increase your funds. Once your done, leave this dead end and continue to the right back on the bridge.
Continue to the left, then up, then into the warehouse. Inside the warehouse you will meet the thrid boss, Rocko. After you defeat him, you must back track all the way back to Sherman Park. Remember that dead end after Grotto Mall? That's where you're going.
Once you enter Sherman Park and fight the random gang members, you will meet your forth foe, the first of the Zombies, Blade. After you defeat him travel all the way back to the warehouse, stopping at Waterfront mall to heal if you need to.
When you get back to the warehouse, continue through the left door and then right into the tunnel. If you push up under the fourth light, you will enter a secret shop. Everything is probably out of your price range, so go ahead and continue to the right out of the tunnel.
Outside the tunnel you will find the second Zombie, Turk. Fight him, then travel up to the next screen and fight the third Zombie, Mojo. Continue up to the next mall.
Go right two more screens until you see the Vacant 3rd Wheel Factory. Enter the door and continue through the inside. NOTE: If you want to go back through the factory for any reason, you can, but you have to make a huge running jump.
In the second room of the factory, you will fight Thor, the last of the Zombies. Thor will only appear if you have already beaten the other three Zombies. Continue through the right door when you're finished, then head up.
In Burb Village you will fight Benny and Clyde for the second time. Go ahead and use them as a positive cash flow if you need to. Continue to the right.
Go up a screen to the gates of River City High and fight Ivan. After you beat him, enter the school. If you can't get in, you've missed a boss, you're gonna have to go back and find who.
In the gym of the high school, you'll meet Otis. He'll yell at you. Beat him then climb up to the ledge and into the door.
Continue upstairs again to the 2rd floor, and you'll meet Tex. Tex is scary, with those crazy eyes and all. Beat him and go upstairs.
See those gray doors on the 3rd Floor? Enter either the far left or far right white doors to enter a secret room. Watch the cut scene, then leave and fight Randy and Andy, the two bosses guarding the doors to the roof.
Well here on the roof of River City High, you will meet the final boss, Slick. If you feel you're not prepared, feel free to return to OAK Hill Mall. Just make sure you do so before entering the door at the end of the 3rd Floor, if you do, you're stuck with Slick, and you won't be able to leave the roof.
Watch the credits, you've won!