This is 1 of 3 trophies where you must get a character to level 30. It is quite time consuming, but you can speed it up if you purchase the season pass. You will be automatically leveled up to level 15 once you have the DLC for this. It will of course, save a hell of a lot of time. Keep playing games to make your way up to level 30. Playing on veteran will help you get there much faster and since you are looking to get the legendary weapon drop, you should be playing on the hardest difficulty as often as possible.
One great thing i found with this was looking for games with elite players. I was level 12 and joined in a game with 3 guys who had hero levels that were over 100. By the time i finished the level, I was now level 30 and also got around 11 hero levels. You obviously bring things down for the others, but if it helps you get to level 30 faster, all the better.