Aquaman can out zone DS from what I have played. I have yet to lose to a DS player and they did constant spams. Just have to time your trident spike well and then you can move in on him if you so please. If not, you can continue to out zone him.
Doomsday is an amazing rushdown character. You can confuse some DS users with supernova MB to get in. You can either follow it up with DF 3 or continue your pressure if you are near a corner. If you get a chance to activate trait while DS is down in the corner, do so. It will help with his wake up. Keep pressuring him until his morale crumbles to dust.
This is about the best way to play against some of the DS users I played against. I don't think I ran into anybody extremely good yet but time will tell.
