You can find this mode under
Multiplayer > Warzone > Playlist > Warzone.
To earn this achievement you need to complete, not necessarily win, three matchmade games of this multiplayer game type (that means no custom games). To get a feel for the mode, try just playing the basic "Warzone" game a few times and the achievement will unlock at the end of your third game. Each match is around 15-20 minutes, so you're looking at around an hour of playtime for this achievement.
If you happen to win on each of the three original maps (Escape from A.R.C., Raid on Apex 7, and March on Stormbreak) you'll also unlock:
Note: If you're having trouble finding a lobby, change your Search Preference to "Expanded" for a better chance to find a game more quickly.
If you feel something is missing, please leave a comment so I can update/correct the solution.