Cages are similar to treasure chests, but require 4 keys and are usually harder to find. Each cage houses characters that may be familiar to you. When rescued, they will appear in the Sanctuary. Visit the Sanctuary from the world map when you have all 12 to unlock the achievement.
You'll need 48 keys to unlock all 12 cages. Keys can be found scattered throughout the world, and bought from shops (up to 6 total from shops). Explore the areas marked with a circle to look for keys and other goodies. Some cages can only be reached with abilities that won't be unlocked until later in the game.
Aurora Village - Hyperduck #1
Archers' Pass - Bastion (Complete One Last Wish for Rainbow gem)
The Glade - Super Meat Boy
Cirromon Caverns - Spelunky Boy (slide required)
Cirromon Caverns - Spelunky Girl (boost jump required)
Abadis Forest - Bandage Girl
Abadis Forest - Hyperduck #2 (slide required)
Sorrowing Meadows - Dishwasher (vine climb & double jump required)
Sorrowing Meadows - Yuki
Blackmoor Mountains - Fez (double jump required)
Blackmoor Mountains - Braid (Red Orb required)
Everdawn Basin - Maw (boost jump required)
In this video, I show the locations on the map, and then how to reach the cages from there. Click the annotations to skip to any friend.