Several different potions are used to transform different characters or give them powers.
The red potion was the first one Lucy found, left for her by the previous mermaid in order to transform her into a mermaid, and give her control over fire and water. It tasted like sea salt, fish scales and sand, among other things, and left Lucy feeling very queasy.
A potion created by Lucy in order to give Jack the ability to teleport. She based it mostly on the red potion, sans the ingredient to turn him into a merman, and it tasted very much the same. Jack seemed to recover from the resulting nausea more quickly than Lucy, though whether that was because of the potion or just him is unclear.
A bottle of potion found by the two on the beach, which Jack drank and said tasted awful.
Another potion which appeared when the blue one vanished, which Jack also drank. The bottle had an inscription in a language which Jack couldn't read, but Lucy could, saying it was from the other mermaid (and several other things). It tasted like syrup, but not in a good way, and gave Jack another power.
A dog biscut Lucy fed to the dog which Jack was unintentionally possessing, in order to send him back into his own body.