I'm sure it's another player, because I've not played local co-op for this game.
Nevertheless, I hosted and re-did, and it popped after Level 9.
Also, TS, for "We Don't Need No Magic - 30G", it can be unlocked in a co-op session with a friend using special attacks to help out. As long as the person getting the achievement doesn't use the special throughout, it should unlock. I solo 1-10, but kept dying at 11. I hosted a game and someone used his special attacks to help kill the boss, and I unlocked the achievement this way.