Lion, wolf, gorilla, bear. Can any of these animals be sufficiently tamed to be a woman's constant companion and go into battle with her?
Well, dogs were invented because someone tamed wolves and got them to do things, so there's that. Theoretically, I imagine it would be possible, or at least feasible to an acceptable level of suspension of disbelief, for any of those animals to be trained from cubhood.
Well, actual wild animals are incredibly unlikely to actually be 'tamed'. Non-domesticated animals that are raised alongside humans (in zoo or rescue type scenarios) are still wild animals and though they might be friendly, they don't have the predisposition towards not harming us and can 'snap' - under stress they will still view us as threats or prey animals. Domesticated animals are called such because over years and years we've selectively bred them and they've independently adapted to us in ways that make it possible for us to live together peacefully. We do have companion animals like reptiles, birds, and rodents that haven't been truly 'domesticated' but are basically chill with hanging out with us anyway. My pet ball python is cool with me because she's never been hurt by humans and snakes her size can't remotely consider humans my size prey, so her reaction is essentially "well, you're warm and non-threatening, so we can hang out", but she doesn't have any features of an actual domesticated animal. Some people have pet foxes but they're known to be fairly aggressive, too high-energy, and super destructive because they're not a wild animal that's suited to forced 'domesticity' (apparently fennec foxes are better, but they're a lot smaller and generally docile than red foxes because of their lifestyle; they mainly eat bugs iirc so they're not much of a hunter/predator type like red foxes). Something like a lion or bear would be the same. It's a predator. If it's not hungry or feeling threatened or territorial it might be curious about you and chill with you. If you raised it from birth it'll probably be happy to. But it's still a predator driven by instincts and not fit to the lifestyle of a companion dog or something like that. Especially when you put it under the stress of war, it's not going to pan out. You can't control them. So realistically I'd have to say no. But are badass wild animals as companions a staple in fiction? Yep. So go for it if it's what you want. There's precedent.
Wolves would probably be your best bet. Gorillas aren't very aggressive, though they can be violent when the need arises. As far as apes go, Chimps are more violent. Lions or bears might work if they were raised from childhood, but they certainly aren't a sure bet. Of course, all of this depends on what is available in your setting. Some things may aid suspension of disbelief.
Surprisingly few generations too. In the 1950s The Soviet Union started an experiment of selective breeding wild foxes for tameness: https://en.wikipedia.org/wiki/Russian_Domesticated_Red_Fox. The project is still going on and they're remarkably different than their wild relatives. After only four generations, they started to see major changes in their psychology: https://en.wikipedia.org/wiki/Dmitry_Konstantinovich_Belyaev#Belyaev.27s_fox_experiment They are currently somewhere around generation 35 or 40 I think.