Here is the full list of all 10 Happy Birthday, Bernard achievements.
Fail on the first level.
Beat the sixth island without refilling your watering can.
Don't waste any bread in the duck minigame.
Beat the fourth child island after standing on the right-most platform.
On the fourth adult island, jump directly from the dead-wood block to the entrance of the cave and back again, without planting a seed.
Beat the first adult island on the right fork before any leaves leave the top of the screen.
Beat the final adult island on the right fork in under 27 seconds.
Finish the game with water still in your can.
Finish the game with all the islands beaten.
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