The first Puzzle Piece is near the start. Move to the right and blow on a blue flower to extract the Puzzle Piece from the ground. Now jump up and bounce off of the Tiki Buzz to gain enough height to get into the wooden box above the start area. Pound on the crate and you can now ride Rambi through the level.
Keep going to the right until you reach the DK Barrel; then jump left and get the K KONG letter while avoiding the swinging spiky ball. If you have Rambi, you can just crash right through the spiky balls.
To get this Puzzle Piece, you will need Rambi. After passing by the checkpoint, crash through the Rambi block to enter a bonus area. Here you must clear out bananas, balloons, and coins to get the Puzzle Piece.
Pound on the DK platform to break open some large crates and jump over to the platform. Before jumping into the barrel, dismount from Rambi and blow on the blue flower to get another Puzzle Piece.
While you are in the background area, you must move quickly across some wooden platforms that fall shortly after you touch them. Jump across on the heads of the Tiki Tanks and get the O KONG letter as you are going. If you have Rambi, just plow through these enemies and jump up before the platforms go down; then get the letter. If you grab all the bananas and the O, then a balloon will appear after the collapsing path.
Once you return to the main part of the level, make your way across some hanging rock platforms. The N KONG letter is above the first one. As soon as you touch these platforms, they start to fall; therefore, to get the letter, jump off the Tiki Goon on the solid platform so you can get high enough to get the N KONG letter. Then quickly head across the falling platforms to the checkpoint.
The G KONG letter is hovering over another falling rock platform. Jump off of the Tiki Goon on this platform so you can reach up and get this letter to spell out K-O-N-G; then continue on.
Pound on the DK platform to reveal some Rambi blocks. Crash through them while riding Rambi. Collect the Puzzle Piece on the other side, as well as four coins and lots of bananas.
As you move across the background area toward the Slot-Machine Barrel, collect all of the bananas that are moving around in circles. Each circle has either a fireball or Tiki Zings in them. Rambi can knock out the Tiki Zings, but you must avoid the fireballs. Collect all the bananas along this background area, and the last Puzzle Piece will appear. Then just hit the Slot-Machine Barrel to complete the level.