I've tried going through Arcade mode 4 different times with 3 different characters and I run into the same problem once per run, at either the 2nd, or 5th match. With Ryu I run into Blanka, he spams his ball dash attack, knocks me down, I get up, does it immediately again. Repeat until I lose. With Cammy, I run into T-Hawk and he does some crazy shit.
Also, I've read up on it that once you get to Akuma, you can face him as much as you want and still get the Achievement. This means you can switch characters, too.