Effect only activates when he destroys an opponent’s monster by battle.
Mighty Warrior only needs generic synchro materials making his summoning fairly easy. Here are some examples of easy level-6 Synchro plays. Blackwing - Blizzard the Far North can revive a level-4 Blackwing monster. Psychic Wheeleader Special Summons himself when you control a level-3 monster.
Quillbolt Hedgehog can revive itself when you summon a level-4 Tuner monster. When you control a level-4 monster, you can Special Summon Plaguespreader Zombie.