Awesome / Brainiac

• In his first appearance -Action Comics #242-, Superman was unable to beat Brainiac. The Man of Steel threw chunks of planetoid at the twelfth-level intellectual until he ran out of planetoid. The whole time, Brainiac just stood still, grinning and letting his deflector shields take the blows.
• The character's most notable one is effortlessly managing to steal Kandor, killing many Kryptonians in the process and possibly triggering Krypton's destruction. The Kryptonians were Sufficiently Advanced Aliens and basically gods to most of the universe, but they were completely helpless against Brainiac, who hardly seemed to notice them.
• In an old 100-pager Action Comics issue (specifically #443 from 1975), the lead story has a sort of Injustice League capturing every single Justice League member except Superman. Superman makes his way to their satellite, melts Sinestro's ring, and promptly wipes up the villains with ease... save Brainiac who takes down Supes, but not before he can free the Flash who frees the rest.
• In Crisis on Infinite Earths, Brainiac assembles an army of supervillains from across the multiverse and immediately conquers several alternate Earths, disposing of all their heroes and becoming a threat second only to the Anti-Monitor. None of the other villains question his authority, except for Alexei Luthor, who he quickly vaporizes for his trouble.
• His androids and machines nearly manage to destroy both Superman and Supergirl during the Brainiac story arc. He also not only beats, but outright curb-stomps Superman in their first physical encounter, and earlier had knocked him out and imprisoned him after detonating a star in his face.
• In the New Krypton arc, he builds an upgraded robot army that manages to kill tens of thousands of solar powered Kryptonians, and Brainiac himself easily overpowers Zod in their brief super-powered struggle. His ship also proves unassailable without help from his own descendant, Brainiac 5, even against a weapon that can outright kill hundreds of Kryptonians as collateral damage. If not for a last second betrayal by Luthor, he would have easily won despite facing Superman, Zod, Supergirl, the Legion, and an entire army of Kryptonians. In fact, his descendant Brainiac 5 and the Legion traveled back in time to stop him for precisely this reason- because in the unaltered version of the events, Brainiac did kill Superman.
• Brainiac 13 pulling Eviler than Thou on every other villain in the universe, outmaneuvering and absorbing Imperiex to become a universe-level threat that even Darkseid is terrified of.
• How feared is Brainiac? In Superman: Doomed, Mongul and Non (easily Superman-level foes in their own right) are so terrified when they hear he is coming that they willingly enter the Phantom Zone to get away from him, suspending their plans to invade Earth.