Free Kong Buddy
Before starting a level add a second player from the 'World' menu. Then press 'Start', select the 'Add/Drop' option, and press A on controller two. Now select the 'Control' option and choose to play as Diddy Kong, Dixie Kong, or Cranky Kong. If you now choose to remove the controller from the 'Add/Drop' menu you will still retain your Kong Buddy.
Metroid
Go to World 4-3, Amiss Abyss. There is a Metroid hiding in the background just before the underwater signpost with the green arrow. You have to swim past the signpost, go all the way out of the cave to the open area where the jellyfish are circling, and then backtrack into the cave. You will have to take a hit from the electric seaweed on the way back to the signpost. Once you reach it, a school of fish will swim up in the background, followed by the Metroid.
Shipwreck Shore Puzzle Pieces
In total there are nine Puzzle Pieces in the level Shipwreck Shore and collecting them all will unlock art.
First Puzzle Piece (1/9)
Go left at the beginning and jump on some wooden boxes. If you then smash them and pull the vine it will reveal a Puzzle Piece.
Boat Puzzle Piece (2/9)
At the first large boat you encounter jump in the water and swim under it to find a Puzzle Piece amongst the green algae that is there.
Secret Room Puzzle Piece (3/9)
On the boat there will be a platform in the middle that will lead you to a Secret Room where if you collect ALL the Bananas before time expires you will get a Puzzle piece.
Hidden Cove Puzzle Piece (4/9)
Go right once you are past the checkpoint. Then jump so you grab the grass and instead of going to the right go left and jump across onto the rock platform to reveal a hidden cove which will have a Puzzle Piece inside.
Yellow Flower Puzzle Piece (5/9)
While you are grabbing the grass you will come across a yellow flower. If you press Y or X near it a brown bag held by a rope will appear, reach the platform to it's right, jump on the enemy, grab him and throw him on the bag in order to reveal the Puzzle Piece.
Bananas Puzzle Piece (6/9)
Proceed until you are forced to go underwater. If you then head to the left and break the wooden planks and collect ALL the bananas you will reveal the Puzzle Piece.
Wooden Boxes Puzzle Piece (7/9)
Once you have collected the sixth Puzzle Piece destroy ALL the boxes in the area to reveal a Puzzle Piece.
Shark Puzzle Piece (8/9)
Jump in the water when you have passed the checkpoint and swim to the algae on the sea floor avoiding the angry shark that is there. When you find the chest press Y or X next to it to real the Puzzle Piece.
Last Puzzle Piece (9/9)
Once you have landed on the springboard raft slam the ground to activate the sail and launch it. You will see plenty of grasshoppers and bananas floating in the air. Collect ALL the bananas to reveal the final Puzzle Piece.