The first Puzzle Piece is right above where you begin the level. To get it, move past the first set of fists, pick up the DK Barrel, and wait until the second fist comes down. Jump up on it, then jump to the left onto the short blue platform while the two fists are apart. Quickly jump across to get the Puzzle Piece. One down and only six more to go.
After getting the first Puzzle Piece, wait until the right-side fist is up and then jump across to the blue platform underneath it. From there, jump onto the top of the second fist just to the right and ride it to a barrel. Jump into the barrel and from there, shoot into a bonus area. Collect a couple balloons, two coins, and all of the bananas to get the Puzzle Piece.
The K KONG letter is fairly close to the start as well. Jump onto the blue platform below the malfunctioning fist. Wait until the two fists below and to the right go down, and then jump down to them, picking up the letter as you fall.
After riding some barrels across a gap and getting coins, you will see the next Puzzle Piece up high. To get it, continue to the right. Jump into a barrel and shoot across to the right. Instead of shooting to the left to another barrel, ride the barrel to the top and then shoot off to the left to land on a small platform. Now jump across several small platforms as you head left. Grab the Puzzle Piece.
The next Puzzle Piece is directly over the first checkpoint. Head right until you reach a pile of rubbish. Get to the top and then from there jump to the left onto a small platform. Jump across to two moving platforms—timing your jumps carefully—and you will collect bananas before finally arriving at the Puzzle Piece.
Head back to the rubbish pile, and from there hover-jump to the right to get the O KONG letter.
The N KONG letter is between two sets of fists. Climb onto the top left one, and as it goes down, hover-jump a bit to the right to get the letter as you drop; then move back to the left to land on the lower fist. Quickly move left a bit more so you don’t get smashed.
Now that you have the N KONG letter, get atop the second fist. From there, jump to a small platform where a Puzzle Piece is waiting for you. From here, you can see the next Puzzle Piece as well.
Move under the wall between the two Puzzle Pieces and jump to the right onto the hands holding boxes. Wait until a box appears on the left hand, then hover-jump across to the left to get the Puzzle Piece.
The next Puzzle Piece is also up high. When you reach the row of four hands and boxes, jump up and get the four coins. Then jump onto the boxes before they are removed so you can get high enough to snag this last Puzzle Piece.
Near the end of the level, you must ride in a barrel. As it moves over the G KONG letter, shoot yourself down to get it. Then jump into the nearby barrel and continue to the Slot-Machine Barrel to complete the level.