The goal is to reach 250 Hero levels, across all of your available roster. That means the actual level system, so starting from 1 and reaching 50 before Champion levels come into play. In the process of aiming towards other trophies, such as 50 hives completed and completing the Iconic Avengers quest chain, you should already have one character at Lv.50 and some others at least around 20. The trophy itself is bugged, as mine unlocked within the early 200s (200-210 range). I was worried, as I had read that it was not unlocking for people after getting 250 or more levels, and that Champion levels also caused some issues. At the time of unlocking this for myself, it unlocked prematurely.
Two things to suggest: try spreading levels among all of your characters if you can, and also try to avoid getting a Champion level until after this unlocks. I do not know if that can actually stop it, or help it, but I did accidentally get one.