Lasso Mastery: Wonder Woman is extremely skilled at wielding her unbreakable Lasso of Hestia both offensively and defensively, notably using it to stop an escaping German spy, to take down numerous German soldiers in World War I battles, to retrain a British terrorist leader, to restrain and defeat General Ludendorff, to hold her own against Ares after getting her sword destroyed, to restrain a resurrected Superman (albeit unsuccessfully), and to even restrain Doomsday himself.
The JLA's first trip to the universe is where Owlman is found hacking computer systems to get the info he needs. There, the JLA fights recruits the Crime Syndicate of America has recruited. Their second trip was when Batman followed Superwoman, and defeats her. After taking out Superwoman, he calls the JLA, and alongside the JLA travels to the moon, to get to the Crime Syndicate's headquarters. From there on, every JLA'er fights against their counterparts, and Wonder Woman manages to even win against her counterpart, Superwoman.
Diana sees Sir Patrick Morgan in the base, who reveals himself to be the true Ares, and tells her of his plan for a world without humanity by having them destroy each other. Ares proposes that Diana help him accomplish his vision of paradise, but Diana promptly refuses, not wanting to kill billions of innocents. Ares then reluctantly engages her in an epic battle while Steve and his comrades attempt to dismantle the plane harboring the mustard gas.
Superhuman Speed: Wonder Woman, while not as fast as Superman or the Flash, can move at inhuman speeds. She was able to make it from the Metropolis Airport to Gotham Port in minutes after seeing Doomsday on television. She was fast enough to get up from her seat, disarm a man of his gun, and toss him across a room in seconds; to leave Lex Luthor's fundraiser before Bruce managed to reach her; to save Batman from Doomsday's thermal attack; and to instantly use the Sword of Athena to slice apart in mid-air a car that Doomsday hurled at her. Indeed, Wonder Woman appeared as a blur when charging back at Doomsday after being knocked back by him. She was also capable of landing blows on Superman, even though she was outmatched.