So, of course you can get this over time as you regularly play the game, but there is a faster way to get this. I tested this after seeing Empoleon Swag's solution for EXtra! EXtra! and it worked.
First, go to Ryu's 7th trial stage. (the stage doesn't actually matter but you aren't likely to accidentally hit this combo to end the level)
Proceed to spam the heck out of the Metsu Hadoken [ (down, quarter turn towards opponent) x2, LB for standard controls) ]
Your ultra combo meter automatically recharges so you can just keep doing this.
You don't have to use Ryu so if you're more comfortable with another character you can use them instead.
It took me about 15 minutes this way starting at 0.