Steelrising

Straight off the bat I'd like to mention that usual tactics of getting in behind bosses to deal more damage is not going to work for this fight. The Centaur will kick out behind it several times if you try to hit him in the buttocks. You are going to want to attack from the side instead, especially since it's also easier to back away from some of the Centaur's attacks when side-on.

Phase 1) Keep an eye out for the canon in the horse's mouth that will shoot flame cannonballs at Aegis. You only need to move to the left/right and wait for the Centaur to shoot it's 4 cannonballs in a straight line where you were standing. Afterwards the Centaur will come to close the gap between you.
- The rider part of the Centaur is going to constantly try stabbing you with its spear when in close range or do big sweeping attacks that will knock Aegis over/back (dependent on your Balance stat), this is easy enough to dodge/block and try get some hits in though. However, keep an eye out for the horse rearing up on its back legs (or the 3 red lines either side of the health bar) as this is your warning to back off immediately before the Centaur does a fast sweeping attack on the side you were attacking it on.
- Explosion and petrification grenades are your best friend here. Explosion ones because they deal a good amount of and enable you to keep your distance, and Petrification because they'll build up The Centaur's immobilisation meter much quicker and allow for a good critical hit once fully immobilised. The Petrification grenades might not be as useful for a Power/Heavy build so feel free to try using other grenades or experimenting to find the right tactic for you.
- You can also use Frost grenades to buy yourself a breather and get a bunch of hits in, just be prepared to throw about 6 (or use the Selenite Momentum move (L1+X)) as the Centaur has a little more resistance to frost than the earlier Titan bosses.

Phase 2) Once you depleted the Centaur's health by half (6 chunks) the Centaur will rear up on its back legs and twirl the spear in the air, setting it on fire before bringing it down and releasing a huge swirl of fire around it. As long as you start backing off once you see the spear catch fire you'll be out of the blast radius in time.
- The Centaur's spear attacks will be roughly the same but it'll sweep much wider and and cause fire build-up on contact.
- Now when the Centaur shoots flame cannonballs from its mouth the balls will follow you wherever you dodge, so keep moving/dodging till you've heard all 5 cannonballs land.
- If you manage to land several good hits the Centaur will point its spear to the ground and dip its head to the ground as flames start coming out of it's eyes and nostrils (on the horse head). At most get in one or two more hits before backing off as the Centaur will kick up it's back legs and jump around in a circle (think a bull at a rodeo) slamming down it's back legs causing an explosion of fire on the ground around it every time it's feet land - it'll only do this about 8 times.

I'd say this fight is more difficult than annoying since alot of the attacks you knock you off your feet, so as always be patient and attack strategically.
Happy hunting and don't forget to loot the Centaur's corpse for the oh so precious loot :)