This site says there 451 achievements: http://d3db.com/achievement#achievement
For the feats of strength there is a thread started here for that: What are the feats of strength in Diablo 3?
I'm not going to copy and paste ALL of the achievements because there is a TON of them. Here are some sources to check out:
- http://ca.ign.com/wikis/diablo-3/Achievements
- http://www.gamefront.com/diablo-3-complete-achievements-list/
If you also want to see the achievements push Y(that is the default key) while you are in game.