3 achievements require you to finish with 300 supers, cross arts and cross assault. You will save time by doing your land 100 quick combo achievement while doing the cross assault.
Go to vs and set rounds to maximum, best of 4.
Look for gems, one will automatically give you meter for being on 25% health, another for 50% total team health. You may need to purchase the gems, but it will save you a lot of time. Probably the next best gem is the one that gives you a big increase for landing the first hit, which you always will.
Set you starting health to 25%, the gems activate at the start of the round. By the time you jump in and land one combo you should have enough to do your cross art. I set Akuma as opponent on 75% health, that's just enough to survive while you gain the last meter you need - just one decent tag combo.
When going for the cross assault finisher achievement, you can also work towards land 500 super arts and it will still count as a cross assault finish. During cross assault, as soon as I activated cross assault I then did a quick combo to get land 100 quick combos.
If you use the gems to start with meter, you can get 300 super finishers in under 2 seconds a round by setting opponent health to 0 and having your gems activate by having your own health at 25% on both characters.
Also during pandora finishers, you can still land a super, quick combo, ex move, launcher, etc to work towards the land 500 of achievements.
I'll add more detail about the exact gems later.