This site says there 451 achievements: http://d3db.com/achievement#achievement 

For the feats of strength there is a thread started here for that: https://gaming.stackexchange.com/questions/66748/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.