Hi BK, thanks for always doing a good job on the fight questions and providing lots of detail.
1: Ostrich vs. bobcat at typical weights
2: Musth elephant vs. alpha male boar at parity
3: AWD vs. brown hyena at exact parity
4: Chimp vs. very big brown hyena at exact parity
5: Two bobcats working together vs. big alpha male chimp
6: Spotted hyena vs. black bear at parity
ostrich vs bobcat (typical weights): The ostrich will weigh over 10 times as much as the bobcat. An ostrich is the world's largest bird, and occasionally defends itself from predators larger & more formidable than a bobcat (leopards, hyenas, cheetahs, etc.) with powerful kicks. Bobcats are quick, agile, & well-armed (jaws & claws), but are too small to single-handedly tackle an adult ostrich. Even if the bobcat leaps upon the ostrich and attempts to mount an attack, it will probably not make enough meaningful headway before tiring out or falling off (as the ostrich will be resisting). An ostrich has great endurance (can run 30mph for 30 minutes straight), and a bobcat does not (relies on explosive action within a small window of time). A bobcat probably won't attempt an attack here against a healthy ostrich. Cats usually trump birds in nature, but this is one exception. Ostrich wins.
musth elephant vs alpha male boar (at parity): The boar will measure almost 5/6 of the elephant's shoulder height at equal weights. An elephant in musth will have a definite strength advantage over the boar, but the boar will have greater lateral movement (front-to-back; side-to-side). The skin of an elephant is about an inch thick, but it has no layer of fat underneath, and can be breached by the boar's tusks (and the tusks of a boar the size of an elephant can exceed 15" in length). However, the elephant will be able to apply a great deal of concussive force with each motion that makes contact with the boar, and the tusks will be able to penetrate the tough hide of the boar considering the strength of the pachyderm. This won't be an easy fight for the elephant, and it will get injured, but the combination of its ferocity (in musth) & great strength will enable it to prevail more times than not. Edge to elephant in musth.
African wild dog vs brown hyena (at parity): The brown hyena is not as powerfully built as a spotted hyena, but it is still an aggressive, dangerous foe. Brown hyenas have very strong bone-crushing bites, and can be confrontational. African wild dogs are slender, quick, and have good lateral movement. Their jaws are strong as well (among the strongest pound-for-pound among canids), and they occasionally overpower large prey items as a team. The African wild dog will have the advantage in speed & mobility, but the brown hyena will have more strength, durability, and a bigger bite. The brown hyena is physically a notch above the wild dog at normal weights and equal weights. Brown hyena wins.
chimpanzee vs brown hyena (at parity): Chimpanzees are strong animals with decent bites, but they aren't equipped to dispatch a similar-sized opponent one-on-one. Brown hyenas occasionally battle other animals, and their comparatively durable builds & bone-crushing bites make them more formidable in battle than a chimpanzee. The chimpanzee might succeed in intimidating the hyena, but it won't have the tools to defeat it in a serious rumble. The chimpanzee may have a small edge in overall mobility (and its use of hands may make it difficult for the hyena to latch its jaws onto the ape's body), but its bite won't have nearly as much effect on the hyena as the hyena's bite will have on it. Edge to brown hyena.
2 bobcats (working together) vs big alpha male chimpanzee: A big chimpanzee can weight 4 1/2 to 5 times as much as a bobcat. Bobcats typically prey on small animals (hares, rabbits, squirrels, birds, foxes, raccoons, etc.), and larger prey items are typically cervids impeded by deep snow. Bobcats usually attack by ambush, and rush in to deliver a killing bite. Chimpanzees usually don't engage in serious fighting with other species (mostly use intimidation or a numbers advantage), but are very strong primates with decent bites. The bobcats can certainly injure the chimpanzee with their sharp teeth & claws, but the ape's use of its hands to grab & control will help it to repel the cats. The chimpanzee will be able to fight back better than a cervid in deep snow will, and will have enough strength & endurance to overpower the bobcats. A bonobo chimp will be small enough to be in real danger against 2 cooperating bobcats, but this big alpha male chimp will be too big. Chimpanzee wins.
spotted hyena vs black bear (at parity): Spotted hyenas are very durable mammals with extremely strong bites. They often do battle with lions & leopards, and can tackle large prey items as a group. Black bears (American & Asiatic) are very strong, have great stamina, & good weaponry (jaws & claws). The spotted hyena is somewhat clumsy in its movements, and won't have a great mobility advantage over the black bear. The hyena may try to land a bite on the bear, but will likely be met with swiping/grabbing paws & large jaws. The bear's sharp claws can cause serious injury to the hyena as it closes in to attack, and the bear's forelimbs can clutch the hyena's body to impede its movement. Black bears aren't practiced at dispatching animals as large as they are, but one will have the tools to drive a spotted hyena away without too much trouble. With few exceptions, an animal with jaws & claws will trump a similar-sized animal that only has jaws. Black bear wins.
Ask anytime; always happy to help!