How to earn the Speed Demon bonus in Super Smash Bros. 64

After you finish an up B move and enter the "helpless" falling state, you can fall through soft platforms by simply holding down on the joystick. This state is the only time you can fall through a platform as if it were not there.

Not all characters can do this. Examples include Kirby (the final down-stroke of his final cutter up B does not ever finish until interrupted by landing/getting hit/blast zone) as well as both Jigglypuff and Yoshi (the two non-jumping up B's). Also Falcon's up B does not make him helpless if it connects with an opponent (but does remove his second (aerial) jump). A related special case is Fox's up B (the fire fox) can also pass through soft platforms during the move itself, when aimed downwards.

In all other cases, you can't fall through a platform per se, so it must be done in two steps: land, then drop through. Given enough practice with the timing, it is possible to perform the two step sequence fluidly and almost seamlessly. The fastest way to drop through a platform from a standing state is to "shield drop" by pressing Z and down on the stick at the same time. It saves a frame or two of ducking animation compared to the normal smash the stick downwards method, and also works while running/dashing.

Not to brag, but I was notoriously good with Kirby. My friends hated me :P Its been a while since I've played, so forgive me if I don't know exact key mappings.

Kirby's strength is not from his power moves (the B+direction ones) but from simple aerial attacks and smash attacks (the A+direction ones). The "drill" attack is your main weapon. Float around the map until you find a target you can drill into the ground. If your opponent sees you circling them, they'll counter the drill attack with a power move. Anticipate whether they're prepared or not, and if they are prepared try your B+up move.

After you drill someone into the ground, they'll bounce up for a few seconds. This is a great opportunity to use your A+up. This will knock weak enemies completely off the map. If not, they'll still be vulnerable in the air. You could just jump up and A+right them for a painful 2-smash combo, which will surely send them flying far away from you. Or you could try B+upping them or drilling them again.