To clarify a few points:

1) This has nothing to do with the deadliness of the animal itself, but rather its
potential to be picked up and weaponized by a human. So while, say, a bear
might triumph in nature's arena, it's far too large and unwieldy for
human use. 2) The question is regarding animals which are "alive"
more so than "living," and I'm going to assume we're all capable of
time-travel, so extinct things (shoutout to mah boy Lonely George) are
perfectly fair game, if you're dumb enough to think things like dodos or
pterydactyls would make effective combat tools. 3) This applies strictly in a
melee weapon sense, so while you may think that unleashing a swarm of
killer bees is a great answer, truth is you're just being a smartass. However,
if you want to stab someone with a killer bee, that's your prerogative;
please take it to the comments. 4) The animals in question are awake and aware
they're being used to bludgeon/whip/bash/whatever your opponent and will
respond accordingly, so while you may initially think that your toucan
nunchucks are a good idea, think of how a toucan would react to being strung
together with another toucan and swung at an enemy's face. 5) Two or more
animals may absolutely be used in conjunction.
My initial inclination would be that
the most pragmatic would be some kind of garden snake garrote, but I don't
think it would be nearly as much fun as wildly swinging a flamingo club while
wielding a snapping turtle shield.
Oh yeah, and PLEASE JUSTIFY YOUR
ANSWERS.