Board Thread:Plants vs. Zombies 2: It's About Time/@comment-21076114-20130919011254/@comment-21076114-20130920222335

Crazyzombie168 wrote: So the only way to unlock plants is by puzzle pieces not by finishing a level? D: Not the "only way." You can unlock regular plants by collecting a certain number of Stars which you only get by completing a level.

Puzzle Pieces in the other hand are what you need and is the only way to unlock the Premium Plants (so far that's how it seems to me) and can also be used to unlock regular plants instead of Stars.