After finishing a multiplayer match, you'll be able to deploy War Assets to any territory that your selected faction is currently waging war in. For this achievement, you'll have to send the War Assets to the enemy side of the battle. You'll know you are doing this correctly as the confirmation will say "Attack" instead of "Defend". Another easy way is to pick the side that isn't your faction color.
Do this at the end of 10 matches and the achievement will be yours.