You'll want to find a ledge by the yellow tree on balboa island, that's your safe spot for this fight. Make sure to bring a basic bow and at least 60 arrows, since you'll need quite a few to get the job done. Grab 5 wild berries too, they're actually super helpful for keeping mama bear distracted when you put them in the blue feeding bin.

The main trick is getting comfortable on that ledge where she can't reach you, and then taking your shots carefully. You might notice your arrows drop a bit when shooting, so aim slightly above where you want to hit. When she charges just back off for a moment, then get back to shooting once she settles into her patrol pattern again.

Tip: if you're running low on arrows during the fight, you can usually collect some of the ones that missed while she's occupied with the berries. Once you finally take her down, you'll get some leather and raw meat for your trouble, definitely worth the effort especially if you need those crafting materials.

Remember the fight might take a few tries to get right, but once you figure out the rhythm of shooting from your safe spot while managing her attention with berries, it becomes pretty manageable. Just make sure you've got enough arrows before starting, running out halfway through isn't fun at all.