I'm not sure if this trophy glitched for me or not, but I ended up getting it while fighting the Invincible Empyrean Sentinel. I had a corrosive, fire and cryo weapon, but no electric one on me at the time. During the battle, the boss takes on specific elemental forms, during his electric form I ended up swapping between all my weapons and shooting him with each one to see which were the most effective and the trophy popped.
I'm not sure if an elemental enemy will already count as having 1/4 elements applied to them or not.
You can basically get this by finding an enemy with a ton of health, have all 4 of your weapons available contain the 4 elements this game has, and shoot the enemy until 4 elemental effects are applied.
I had read of a glitch that allowed you to shoot a dumpster in Concordia with all 4 weapons to earn this trophy. I tried it and it didn't work. So I imagine this got patched.