If you're inclined to use it, in Arcade (as well as Tutorial and Story) you can taunt your opponent once per round to gain 100 Heat. You can use this to either just get in a few powerful distortion drives or Rapid-cancel combos, and perhaps close the final round with an Astral Heat.
If you can land it, an Astral Heat is almost recommended for the final round, simply due to the increased health of Hazama both for being Unlimitted and for having that life drain effect. It's better not to let a fight like that drag on.
Excluding that approach, part of the battle is a mind-game. There's always the risk of huge combo damage he can initiate very easily. A lot of this starts off with his Rising Fang, which is one of his most vicious attacks due to its high priority and invincibility frames. It punishes standard approaches very easily. Ouroburos also can come out pretty fast and usually never ends well. Furthermore, there's the omnipresent fear of his life drain. It's actually not too dangerous in terms of how much damage you take (his own attack power eclipses it too much for it to have a real impact), the real threat is that it makes blockstrings and unsuccessful attacks much worse for you.
The combination of his Rising Fang, his Ouroburos, and his life drain makes the more successful approaches involve countering his assault. In particular, abusing your own invincibility frames (Ragna's
Infernal Divider D version can clash Rising Fang and still hit most of the time) to intercept his attacks works fairly well. Unless you can get some good tech trapping in the corner (Ragna in particular has a nice
B → D → Gauntlet Hades combo that works very often against Hazama air-teching in a corner), you probably also want to end such counters with Hazama being a fair distance from you.
While at a distance, keeping wary of Ouroburos (an instant guard on your part can turn things around very swiftly) and using either projectiles or advancing attacks (like
Hell's Fang → Additional Attack) to punish any openings will often work very well. Usually, it helps more to use attacks that knock him down again and don't leave you vulnerable for too long.
I'd say the important thing is to focus on landing your hits rather than maximizing the damage for any particular opening. If you can score a high-damage combo, wonderful, but sometimes you can settle for just the 1100 or so damage from your advancing attack or invincibility frame attack, as long as you keep landing it. You can even land these kinds of attacks successively if you time them around his wake up attacks.