Completing the Game Quickly
To complete the game quickly, take the warp zone in "World 1-2," (to access the warp zone, run atop the highest point in the level. Continue running until you reach the end of the level and are dropped into the warp zone: warp to "World 4-1"). Beat the following level and access the warp zone in "World 4-1," (again, access the warp zone by running atop the highest point in the level until you are dropped into the warp zone). Warp to "World 8-1" and beat the remaining levels.
Easily Avoid Bloopers
To avoid the pesky bloopers in the underwater levels (the white squid-looking creatures), simply walk along the ocean floor. The bloopers will never float close to the ocean floor, giving you a safer passage throughout the level.
Completing World 8-4 Easily
If you find yourself constantly warped to the beginning of "World 8-4," you may not realize you must go down certain pipes to progress through the level. At the beginning of the level, skip the first two pipes, jump over the lava pit and take the next warp pipe. Skip the next four pipes and jump over the lava. Jump around the floating pipe to make a hidden block appear; use the block to reach the floating pipe. Go down the pipe and skip the next three pipes, jumping over the lava pit and going down the following pipe. Swim through the ocean portion of the level and skip the next pipe. Jump over the lava pit to face off with Bowser. Jump over him and touch the axe to make him fall into the pit of fire to beat the game.