Oh, there have been a LOT of trophies/achievements that I've looked at and gone, "Ha ha, not happening!" and thus haven't even bothered with them. So, hardest one I have gotten? Probably that "Time Travel Will Tell" from Black Ops Shangri-La, followed closely by "Cryogenic Slumber Party" from Moon. The reason "Time Travel" was harder was because it took four players working together, so my two friends and I had to drag a willing fourth player into the mix. And since he didn't care as much about the trophy as we did, it was hard to keep him from running off and ruining everything because he was getting bored.
Most annoying:
Hands down it was "Acquire Waffle Weapons" on Der Reise in World at War. I HATED this trophy. I became an expert on this map because I spent HOURS by myself constantly hitting the box, hoping it would give me the weapons. There is no skill involved in this trophy. There is no gameplay involved in this trophy. It is pure luck. You stand there and WAIT for the game to give it to you. And if the game doesn't want to give you the three weapons, tough luck. I was so relieved when I finally got all three. Any trophy that is based solely on the game and your luck, not skill, is a stupid trophy.