During his hyper armor, just keep smacking at him by tapping square. It will keep interrupting his attacks. If he gets you in the corner, it can be very difficult to get out, since the CPU reacts to your button inputs :P However, you can push back against your opponent by using 1 Bar of your Super Meter during a block. It's R2. For example, Doomsday attacks, you're blocking his string--press R2 and he'll be shoved to the other side of the screen, giving you more room to move. Learn a big combo and just try to nail him with it whenever you can. Also, watch out for his "Fist Pound" move. It hits overhead, then low VERY quickly, which means it MUST be blocked high, then blocked low within like a tenth of a second. Some general tips. Hope that helps.
I find Hard easy, but yes, Doomsday can be a real b****. His shield is what i hate, other than that, i can take him down. What i do when he has his shield up, i try to hit him and he deals a little damage, maybe like 1%. If your using Batman i suggest using his parry, it works, it damages him, other than that try to stay away from him.
Double, double toil and trouble; Fire burn, and caldron bubble.