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You can go back and re-kill any boss you encounter, allowing you to farm the legendaries they can drop(a certain load screen text bar states this exact thing). I haven't heard anything about the legendary drop rates lowering on any bosses after killing them in the story mission......except for the warrior. If you kill the warrior on the actual story mission, he has something like a 75% chance to drop one of 5 legendaries. Not sure about that, seems more like 40-50% chance in my experience, but still pretty good. BUT, after you kill him in the story mission, then go back to farm him in playthrough 2.5, or in first playthrough after activating TVHM, his legendary drop rate plummets down to 1%.
After multiple runs through the game, it's my OPINION that drop rates are in fact higher during the quest. Most of my legendaries came while questing, which actually sucks. Even seen a level 7 infinity pistol? itt's like having an infinite spit ball shooter lol
Yeah I'd have to agree on that...most of my legendarys came on the first play through of my characters I've gotten 2 different grenades, a pistol, a shotgun, and an assault rifle all under lvl 10...epic spitball shooters indeed lol