At first, this battle seems ne’er insurmountable. Deathstroke is an extremely deadly adversary, and any frontal attack is met with an assault of attacks that seem to destroy Bats in seconds. Because of this, you might be tempted to fight defensively, but this tactic is ill-advised. Instead, going on the offensive is recommended, but you need to be careful. Every attack he throws your way can be countered, but if you counter it too early you’ll take a bunch of damage.
For his first two phases you should attack non-stop, only hitting the counter button when either he’s about to strike you or you’re prompted to by the screen. If you hit it early, the prompt won’t even show up--so just play conservatively with the counter button while you liberally pound attack.
His final phase might as well be a full-blown quick-time event. Any time you attempt to hit him you're thrown into a cutscene where you need to counter between one and three times. After a while, Bats will land a blow and you'll be put back in control. Just keep pounding attack and countering once you're prompted and you'll end Deathstroke before too long.
For more tactics here's our full Batman: Arkham Origins boss guide!