The Full Arsenal achievement is awarded for collecting every piece of equipment in the game, and is worth 15 gamerscore. This includes all weapons and costumes.
You can see the equipment you have collected so far by pressing and scrolling to the Collectables tab. From here you can scroll to equipment.
Note that once you have obtained a piece of equipment, there is no requirement for you to keep it in your inventory. The game will acknowledge that you have obtained the piece and keep track of it! This is useful if you are running low on cash; you may sell any unused pieces of equipment without sacrificing the achievement.
Many pieces of the equipment in the game are missable. For a full guide on equipment locations, view the complete walkthrough!