There's only one trophy in Borderlands that actually requires you to go online with other players, which is the one that needs you to play with a Gearbox dev or with someone who has the trophy already. There is a trophy for defeating specific bosses in co-op, but that can be done with two controllers.
Overall, I really enjoyed the game, but the story is bleh and it can get a bit repetitive if all you do is missions, since there's not a whole lot of variety there.