You need to kill a enemy God with your ultimate/4. This can be done over multiple matches.
Your ultimate doesn't do amazing damage and it's also pretty hard to aim.
I suggest playing Arena where everyone is together and maybe letting your team initiate, then you can jump in to do some damage and try to snipe the opponent when they go to escape.
To check progress outside of a match go to your profile and then the "Achievements" section, next go to "Combat Practice" witch is the one with the two swords.