You Can Find Fight Records On The Main Menu -
It Records All Your Online Stats!
Wins/Losses/ Number Of Times High-Punched In The Head
Clicking On Them To View Them Is Enough, The Achievement Pops.
The UI For This Game Is Certainly Confusing To New Players, Just Make Sure To Pay Attention To Tooltips On The Main Menu, And You'll Find Everything Easy Enough.
Goodluck!