This walkthrough was taken from here
Map is from here

1.Starting at room 1 go straight down to room 4
2.Place a bomb next to the brown brick the blue push button is under.
3.Push button to see warp point to room 5 get half of white key
4.Go right to room 7 and kill all guys to open door going up.
5.Go up and left to room 9 and then into room 3 to free yellow key.
6.Go get the yellow key and head up to room 12
7.Use yellow key to get in room 13 and get power push.
8.You can now push block in room 13 to get to 14 for extra coins and life.
9.Head to room 17 and warp to room 18
10.You can then head up to room 20 to buy the map, or just use mine
11.Go to room 21 and kill all the guys to open door.
12.Go to room 23 and write the pattern down, you will need it later
13.Go to room 22 push center block to expose blue door button
14.Go to room 24 and kill all the guys to get block to move. Push blue block down onto button in front of door to open other door
15.Go to room 25 and push center brick to expose hidden door button.
16.Go to room 27 and kill the Boss
17.Go to room 28 and get the password for room 15
18.Go back to room 15 and enter password
19.Go into room 29 and get red key
20.Go to room 19 and unlock the red door.
21.Go through room 30 and 14 and into room 31 push block onto floor button.
22.Go to room 32 and get super bomb. Use it to get back through room 31
23.Go to room 6 and use bomb to go down into room 33
24.Kill all the guys to get into room 34 then go down to room 36
25.In room 37 one of the block will turn into a guy, kill it to open the door
26.Go to room 42 blow up all the crack blocks to reveal another door button, push the blue block on top of it, it will make so you can move the other blue block of the botton that blocks the door.
27.Go to room 45, if you need extra life there is some in room 46
28.Go to room 47 and then 48 kill all the guys to get to room 49
29.From 49 can warp to 11 if you need extra life, go to room 51
30.Push button hidden in center of room to open door to 52
31.In room 52 push blocks to position shown to you in room 23
32.Go up to room 53 and push button to move block out of way. Go back to room 45
33.Go through rooms 54 and 55 back into room 53
34.Go up into room 56 if need extra life blow up cracked bricks at top and push center brick out of way.
35.Go to room 58 and fight boss. To kill him you need to plant bomb, and then when he shoots at you blow it up just before his bullet reaches it. This will make his bullet go back into him and hurt him.
36.Go to room 60 and get the raft.
37.Go to room 35 and use your raft at the dock to go to room 61
38.Go up to room 62 to get green key
39.Go down to room 64, use extra life if you need to.
40.Take raft through the following rooms 65, 66, 41, 40, 39, 38, and 37 to get to room 36
41.Push button to move blocks and go get purple key.
42.Go to room 33 and open green door.
43.Go through rooms 67 and 68 to 69
44.In room 69 rotate block with bombs and line them up so when you push button the shot bounces up to the flashing half circle
45.Go to room 70 and get the black key.
46.Go through the following rooms 69, 68, 67, 33, 6, 4, 3, 2, 15, 16, 17, and warp to 18
47.Go up to store in 20 and buy the orange key
48.Go to 19 use raft to go to 71 and warp to 72
49.warp back and head to room 4, you should know the way by now.
50.Go into room 73 and push buttons to open the door.
51.Go into 62 and through orange door into 72 and then through blue door
52.Go to room 75 and get extra life.
53.Go down to room 77 and fight last boss. In order to kill him you have to get the cannon in the center to shoot him in the head.

Map (click to view full size):