You earn coins in the game by completing levels, albeit a very small amount per level. You earn 10-20 coins per level and will definitely earn 2500 total coins when 3-starring all levels. It is recommend that you first purchase a new monster to unlock the "Curiosity Killed Monsters" achievement, then buy a pack of 3 solutions to unlock the "Keep em' coming" achievement. Buying these two items first will ensure you unlock the store-related achievements with minimal effort. Right when you begin the game, you are given a free 750 coins. Use it to buy a monster to get the "Curiosity Killed the Monster" achievement out of the way.
You can find the Monster Island store at the main menu of the game.