The OP assumes “1v1 combat”, so I’m assuming that the critter, for whatever reason, wants to hang around and fight, rather than fleeing much faster than you can give chase. In other words, we’re not asking what you could expect to eat if left in the wild to hunt with no tools.
Given that rather artificial limit on the scenario here’s how I think it stacks up …
Among land animals the small herbivores are pretty easy. Anything cat-sized or smaller would be easy to kill. e.g. a squirrel, a bunny, racoon, etc. There are hundreds of species in this category.
A baby or pygmy deer, e.g. herbivores up to maybe 50 lbs, is probably doable, but you’ll take some battle damage along the way. Herbivores bigger than, say, 75 lbs will be able to fight you off essentially idefinitely. They also probably have better pain tolerance than you do, so in a dedicated scrap you’ll cut and run before they do.
Once we get to land carnivores it gets tougher. A 10 lb alley cat, even though a domesticated species, will put up a spirited fight. If you don’t shy away from getting thoroughly bitten/scratched, you can certainly break its neck or back with a twist. IOW, it can’t kill you, but it can create enough injury to make you give up the fight.
Same story for dogs. A Dachshund or Chihuahua is an easy kill; one twist & it’s over. A Scotty or Spaniel less so; you’ll need to kick in its ribs or break some limbs to slow it down & then break its neck for the coup de grace. A Doberman, Shepard or Mastiff is gonna be a real fight to the death for somebody, again assuming the animal is motivated to fight rather than flee.
Wild carnivores are similar, but the max size you can take out is smaller. A bobcat is roughly the same size as a spaniel, but worlds apart in combat capability.
Any of the primates bigger than 15-20 pounds will kick your butt.
Birds are inherently much lighter built, and it doesn’t take much to break a wing, at which point they’re doomed. And the same points about herbivore vs carnivore applies. A small crow, a small hawk, and a big pigeon are all the same size, but very different contestants. All three will die at your hands, but I bet you’ll be bleeding in several places before the hawk succumbs.
For fish, a critical question is choice of arena. In shallows adjacent to shore you can kill almost any fish < 100 lbs by slinging it onshore & just waiting. Away from shore getting a grip on, much less killing, even a 1 lb fish is gonna be tough. Once you do grab it though, it’s toast.
As noted by others, you rule the insects, worms, and other small mindless critters.
If I was to summarize all the above, I’d say that you can kill pretty much any herbivore < 75 lbs and most carnivores < 25 lbs. For particularly domesticated species bump the poundage a few % and for particularly fierce or smart or well-armored ones, lower it a bit.
For critters 20-30% larger than that, you’ll win some times and the rest of the time it’ll be a standoff.
At double that size, you win occasionally; most times you get wounded pretty good, perhaps fatally in the absence of medical care (ie in the wild).
At triple that size, you lose every time; the question is whether the animal remains behind to finish you off, or is content to gore you and wander away while you bleed to death.
Now change the scenario to add even primitive tools like a club or a spear or a teammate, and the whole game shifts. Which is why we’re on top of the food chain despite being utterly unable to catch a wild bunny.
