You can access the quick battles from the main menu. There are 9 in total. This used to be unobtainable because winning the last one would crash the game. It now unlocks a character and the achievement. If like me you had "completed" all battles but it didn't register, simply re -defeating the last battle will unlock the achievement for you.
As for actually winning the battles, the battles start off easy and become increasingly stacked against you. The opponent will have a lot of extra health. You will need some luck. The perks you are given are random, so if you get bad ones simply exit the match and start a new one. In particular, I think the last few battles are unwinnable if you don't get the "attack harmony" perk. With that, you only need to pull off 2 fully charged attacks to take out the last opponent. Keep on restarting the game until you get it and mulligan your entire hand for attacks or things that can be made into attacks. Other abilities that are useful are "+ 1/2/3 attack" and "-1 attack cost", but I beat the match with only "attack harmony" and all other perks were junk.