Successfully complete the Pooh and Roo levels to unlock the Owl and Eeyore levels.
Successfully complete the Owl and Eeyore levels to unlock the Rabbit and Tigger levels.
Successfully complete all other levels in the game to unlock the last level.
Successfully complete the final level, then replay any level to play an alternate version where you have to catch enemies in the various locations.
In Tigger's dream, when you have to catch his stripes, run out of the haunted house when the clock is still ticking. Go back in and you will have unlimited time to catch the stripes.
Once you complete level, go back and do "Bravest Of Them All". That is where you have to catch all the Heffalumps and Woozles. Catch every single one in the dream and it will say "You are the Bravest of Them All!"