Can be done in any jungle, cave, or temple level

Many platforms in jungle, cave and temple areas have a tiny slope at their edge, which allows DK and Diddy to get a horizontal jump-speed boost. Just pick up a barrel, run to the very edge of a platform, and press jump at the last possible moment before you leave the platform's edge.

To be successful with this trick, your timing/positioning needs to be perfect, as there is no room for error. If you jump too early, there will be no speed boost, and if you press jump too late, you'll just fall. Not every platform edge allows barrel boost jumps, either.

Notes:

If you bounce from an enemy whilst barrel-boosting, you can extend the boost!

An easier way to get the barrel-boost effect is to jump while holding a barrel on any slippery slope in one of Gorilla Glacier's ice or snow levels.

Due to the design of certain platform edges in some level archetypes, a speed boost can be achieved by jumping at the very edge of a platform whilst holding a barrel. The timing/positioning is critical in attempting this trick. The 'B' button must be pressed at the last possible moment before falling from the platform, otherwise the jump will have no boost in speed.

Can be done in any non-aquatic level

To add a little versitility to DK's hand slap move (Down + 'Y'), try pressing Down, Y and either Left or Right simultaneously. If performed correctly, DK will slide in the direction you pressed as he does his hand slap. The timing is tricky, but this can be a handy way to knock bananas out of baddies without having to slow down too much.

Can be done in any level with one-way plaftorms

If you thought DK's hand slap was limited to when he's standing on the ground, try this trick out. In any level with platforms that can be landed on by jumping straight up through the underside, try jumping so that DK's height comes just short of landing him the platform above, then execute his hand slap (Down + 'Y'). When done just right DK will do his hand slap as he descends, setting up a big surprise for any baddies lurking below.

Can be done in any level with a Klump on a plateau

Diddy might be a relative lightweight, but his jump attack can still overcome a Klump when done at opportune moments. Each time Diddy lands on a Klump, both of them are knocked back, but Diddy is quicker to recover. With a series of quick jumps, the Klump will gradually lose ground, and if the Klump is knocked to the very edge of the platform, he'll lose his balance and fall to his doom.

Can be done whenever controlling Rambi

One of Rambi's hidden abilities is a horn-boosted jump which gets him around 20% extra jump height. The timing is difficult and hard to explain, so it will probably take a fair bit of trial-and-error. The idea is to press 'Y' to initiate Rambi's horn attack, but to then press 'B' so that he jumps right as he leaves the ground from the horn attack. When done correctly, the sounds from both Rambi's horn attack and his jump should be heard at the same time, and Rambi's jump will receive a vertical boost.