Here is a list of heroes that require the hero to use their ultimate 20 times. It's just a straight up usage. No need to hit anything or kill. So ideally, you could cycle through all the heroes on the list that you own and just fire off the ultimate. After about a little over 3 hours (~200 minutes), you can have up to 14 or so omega points.
Captain America
Cyclops
Deadpool
Hulk
Moon Knight
Mr. Fantastic
Nova
Punisher
Rocket Raccoon
Silver Surfer
Starlord
Venom
Vision
X-23
If I missed any, just list it in a reply and I will update the list. Enjoy!