I don't know what quest you're referring to, but do you need to damage, but not kill, these targets?

If so, here are some things you can try:
- Unequip everything. Buy a garbage lv1 weapon. Auto-attack the target. Hopefully it won't die.
- Switch to a mage job. Auto-attack the target. Mage auto-attacks are LAUGHABLY weak. The last time I tried this, my WHM could juuuuuuuust barely kill a lv1 target with a single auto-attack.