Shortly into the game, you will find a gem and get a tutorial for applying it. This unlocks your first gem slot for free. You then are able to spend earned currency on 2 more slots for the trophy. It costs 1000 per slot, so you need 2000 to unlock the third slot and get this trophy.
You will earn currency mainly by doing story quests. Occasionally an enemy will drop some currency that you can hold R1 to pick up when standing over it. Normally I get 50 when this happens, but it doesn't happen too often. I spent a lot of time messing around, going after champions and not doing quests. As soon as I switched back to quests though, I got a lot more and was able to buy the required slots.
You buy the slots in your Gear menu, under each item of gear.