I don't have it totally figured out, but I ended up fighting a few Darkseid's and found a few things. Step one - Don't jump against Darkseid, the laser's hitbox is roughly the size of Europe and will catch your shins everytime.
Inch forward like any zoner. How close you are to him will determine what you can do. From full screen, nothing. From about a third, you can safely call a drone after ducking a laser, this should help you close in. When you're just outside of his low laser range, you should be in position to punish after a ducked normal laser. This is also where you probably start seeing MB lasers and low lasers to try and push you back. Try not to be baited into jumping (something I preach but still constantly do because I'm an idiot).
Most Darkseid's I've seen like to retreat until they're at the end of the screen and then pull an air TP into a jump kick/stomp mix. Fortunately, Brainiac's D2 can catch a TP easy so long as you are watching for it and ready. Punish those mistakes, keep the pressure up once you have it. Try going for more cancels into Beta bomb than max damage off of combos so you can keep him in one place. Hopefully your opponent is one of these online zoners who melts when tossed in an actual fight.
