This is a military empire quest. Empire quests are activated in the campaign automatically or in a scenario by selecting the 'Empire quest' checkbox under 'advanced setup' and 'gameflow' as you set up the game.
Empire Quests can be viewed in game by bringing up the radial menu with the Y button and selecting "Objectives".
To Unlock The Warmonger:
- Enter war with another player
- Kill 6 units belonging to another player
Rewards (For being first player to finish):
- Receive a tier II unit at the capital colony
- Meet another player