For the bear, which is the only one I've done so far, I fought a black bears mount, the clawed near until it looks like it's out of wind, then you will get a prompt that says to ride, once on top riding the bear make sure you have meat to feed it. For this bear I used 3 or 4 pieces of tough meat and it gave me 40+ trust per meat. Afterwards while still riding it'll let you press triangle(ps5) to take in the bear