Similarly, me and another guy agreed to do the "Bully" and "Underdog" achievements and couldn't get them. He killed me at lv10, lv11, and lv12 (with me at lv1), and then I killed him at lv12, neither of us got either achievement. We tried again with him at lv20 and me at lv10, and once again, neither of us got either achievement.

In case you don't know:

"Bully" - Kill a demigod 10 levels below you.

"Underdog" - Kill a demigod 10 levels above you.

I figured, I get all my favor points from winning games and getting the lv20 and the "Win the Game" (Initiate?) achievements.

Yeah there is:

Under the main multiplayer menu, there's an option "My Account" which brings up a webpage showing what achievements you have on that account from online gameplay (doesn't show single player achievements there).