The Stone and Bouncy Ball are unlocked by default at the start of the game.

Iron Ball: Beat any well with the Bouncy Ball. Jewel: Beat Well 3 with the Iron Ball. Matryoshka: Beat Well 4 in under 1m 10s. Wooden Fish: Beat Well 6 in under 1m 05s. Watermelon: Beat Well 7 in under 1m 10s. Plate: Beat 5 different wells with the Matryoshka Egg: Beat Well 8 with the Matryoshka. Mutagen: Beat Well 10 with any stone.

Note: I can't find a reliable source that explains how to unlock the Plate.