Only player 1 in local co-op and the host with online co-op can get achievements.
Microsoft and Sony both have requirements about tracking if players are present when game events are initiated, to prevent achievement 'abuse' (ie dropping into a game just before the end fight and letting someone else kill the boss to get the final achievement). However, D:OS wasn't designed to keep track of which player started events (or which character, for the most part), and it wasn't feasible to add that for the Enhanced Edition, so it can not unlock achievements for the second player.
The PC version works the same way, at least for local co-op (don't recall for online).
