Kingdoms of Amalur: Re-Reckoning is a big game with a lot to do, as well as a good amount of freedom in how you go about doing those things. As an example, there are tons of characters to talk to (the “lots to do” part), but you can also decide to talk to any of those characters while not wearing any clothing (the “freedom” part).
The Streaker Trophy rewards you for doing just that. In fact, this could very well be the first Trophy you earn in the game.
Within minutes of your “Awakening,” you’ll encounter a gnome named Encel who’s in a bit of a pinch. Once you get your first taste of combat and take out some guards, you’ll be able to talk to Encel. Before you do, simply go into the armor section of the inventory, remove whatever you’re wearing (just a Tattered Shirt and some Worn Leggings, if you’re this early in the game), then talk to Encel.
Of course, the NPC doesn’t have to be Encel. You can simply remove your clothes before talking to anyone in the the game and the Trophy should pop. Encel is, however, the first NPC who gives you the opportunity to acquire the Trophy.
So there you go. That’s how you earn the Streaker Trophy in Kingdoms of Amalur: Re-Reckoning.