To destroy enemy troops with your troops, you need to move your 'Rally Troop' into the area of the enemy 'Rally Troop' or just the enemy troops and your troops will attack them. When your troops attack the enemy troops, they will die along with them. This will likely unlock through normal game progression.
You can unlock this during a quick match and have a second controller connected to make this achievement extremely easy.
To unlock this achievement, you need to send your troops to their death by having them attack and kill the enemy troops 50 times.