There are 40 coins in the game total. By doing this achievement you will also naturally unlock
World 1 - 15 Coins
5 Coins - Forest Follies level
5 Coins - Treetop Trouble level
1 Coin - in the tutorial
3 Coins - from talking to the apple sitting on the bridge
1 Coin - hidden, after you defeat Floral Fury next to the axehead dude. Check spoiler for picture
World 2 - 13 Coins
5 Coins - Funfair Fever level
5 Coins - Funhouse Frazzle level
1 Coin - Go to the Aviary Action boss fight and keep heading upwards and go all the way around the mountains until you come out near Grim Matchstick, then head back to Aviary Action and head down across the bridge. Talk to the pink-faced doughnut for the coin. This will also unlock
1 Coin - Just south of the Grim Matchstick boss is a guy juggling, you'll need to parry 4 times in a row without hitting the ground. This will also unlock an achievement if you do it 5 times. Go to the Funfair Fever level and at the start use the trampoline to get onto one of the walls, wait for a pink balloon and just keep bouncing off of it. Return to the juggling guy after to get your coin
1 Coin - hidden next to Funhouse Frazzle. Check spoiler for picture
World 3 - 11 Coins
5 Coins - Perilous Piers level
5 Coins - Rugged Ridge level
1 Coin - hidden to the left of High Seas Hi-Jinx boss fight, behind a tan building. Check spoiler for picture
Inkwell Hell - 1 Coin
1 Coin - hidden to the left of the entrance of the stairs. Check spoiler for picture
And that's all 40 coins. After buying the coins you can also knock out an achievement for buying all items from the shop!
Here is a video guide for those looking for one, all props to
Maka91 for providing it