My Syringe is equipped as my weapon and I keep killing the beasts, What should I do exactly?
Did you edit your Attack score? Attack is compared to Defense and the ratio between those multiplies the base damage for whatever you're attacking with. Stupidly high Attack scores can multiply damage massively, and stupidly high Defense scores can reduce HP damage to zero even on a hit. You see both in the third Shakala fight. The syringe has a tiny base damage, like 1 HP, but high enough Attack scores can multiply it enough to whack anything you hit.
Physical attacks normally always hit. There's a chance you might miss, and a separate chance the target might dodge it. A successful hit will still deliver any extra effects like the tranquilizer or Poison even with zero HP damage dealt. In the third Shakala fight if you have a Poisoned weapon and manage to both hit her and not be hit in return, the Poison does like 10k HP despite zero damage from teh weapo
Even if you did edit Attack, equip the tranquilizer syringe to the Imp if you have it and use Guard for the MC. If you don't have the Imp and edited your Attack, you're kinda screwed...and if you didn't edit it and critters are still getting smeared, that might well be a bug.