I used to be a complete achievement hoarder back in the days when I used to actively use my 360. I managed to get over 20k worth of gamerscore and I always tried to get whatever achievement possible. Then after I quit using my 360 I shifted towards trophy hunting on the PS3, and then became a trophy collector for a year or so.
I have since stopped because it's honestly pointless other than proving you can spend ridiculous amounts of time to get a specific trophy or multiple ones. (Platinum i'm talking about YOU!)
As for my proudest achievement on the 360? I don't know because I don't remember most of the achievements I got on that console. For the PS3, my two proudest trophies are platinum in Demon's Souls and Dark Souls. I love those two RPG's and played both to the point where I know everything about the game from the lore, to the locations of items, treasures and other things. Also getting Platinum in these two games is very difficult because it requires lots of grinding and many playthroughs. My third proudest is probably Dead Space 2's platinum, simply because Hardcore requires a lot of patience and time, and I only managed to get it after replaying the game so many times on hard to get all the other trophies and knowing everything in the game.
Yeah I have a crazy gaming life, and i'm honestly not too proud of it. In general i've spent too much time getting achievements and trophies, (especially platinums) and just gaming in general.