Not much is known about Rex Stewart, the living battle axe known as Warhawk. However, in the short time he's spent in comics and cartoons he's established himself as one of the toughest, meanest fighters in the DCU.
As a member of the future Justice League, Warhawk regularly defends the planet against all sorts of maniacal and devastating threats, the worst our future has to offer. Shape-shifting robots, cyber-warloks, mind-blasting aliens, no matter what comes his way he spears the problem head on and shreds it with gleaming Nth metal talons.
Warhawk once wrestled with a missile until it cried and exploded. After pretending to be dead for a while (because he's stronger than death), he was back to punching super-villains in the face with his pecs.
To stay in top form, Warhawk spars regularly with Big Barda. One time I saw Barda get super-pissed and punch a monster into the sun, anyone who can survive training with her has to be tough.