Begin playing one of your game saves with a low battery charge on your remote to initiate a message from Cranky; he will warn that your battery is low and award you extra lives to help you out.
After you've beaten a boss for a given section of the island, head back to the Extras Menu. You'll have unlocked a bonus music gallery that features the tracks played in the levels of that particular section. It's also worth noting that you must defeat the boss yourself; if you use Super Kong to get past the fight, you won't unlock the music.
Beat every "-K" level (get K O N G on every level in a world) and beat the game. When you do, a golden temple will show up on the world map. Beat the level there and you'll unlock "Mirror mode," a very difficult way to play through each level, in which Diddy can't be used, you only get one life, the level is reversed, and you can't use items.
Beating the game unlocks the Banana Temple, but it won't be accessible unless you do a few things first. To gain access into the temple, collect the K-O-N-G letters in every world and get the orb in each of the world's temples. Once you've collected all the orbs, the door to the Banana Temple will open.