I’m planning out a shirt story set in a medieval alternate universe where a small troop of characters hunt down a mutant beast. Any tips on using swords and arrows and such against a creature similar to a mutant lion or tiger?

Yeah, don’t. A sword is a weapon designed to kill another human being, it’s not a hunting tool. As you may have noticed, people are not particularly adept at clawing your face off. When that’s a consideration, you’re better off looking at a lance, pike or some other polearm.

Those should keep the enraged, wounded, and (hopefully) dying animal far enough away that it can’t seek bloody retribution on members of the hunting party.

Other than that, the best advice is just, “poke it with sticks until it falls over.” This one isn’t that much more complicated.

If the critter requires a specific sword to kill it, your best bet would still be to skewer it, wait for it to wear down a bit, and then deal the killing blow with the required weapon.

Bow hunting is a completely different kind of approach that favors parties of two or three people. You take a shot and then follow the blood trail until the animal wears itself out and expires. Finding the animal is usually the hard part. At least that’s how it normally works. I’m not sure about bow hunting apex predators, but, I have a feeling that could get massively out of hand, fast.