Apollo would never beat Thanos in a million years. And I've said this before, but usually saying "Who can the Authority beat?" is basically saying "Who can the Doctor beat?" A few would be able to hang out in the "herald-level" section of the restaurant (Angie, Apollo, Jack with the right conditions) but none but The D are near Thanos. If they used Carrier doors, all of their resources, and basically bought time for The Doctor they coudl probably do it...but everything would have to go right and I still say Thanos wins more often than not.
But the Doctor's matter control is damn close to limitless, and all he has to do is think about it. Since he once grew in strength and size many hundreds of times, I'd assume he could simply make himself a Class Infinity and throw Thanos to the next galaxy or at least knock him out or something. He's also sent people to different dimensions and traveled time. He could go back to when Thanos had a self-defeating personality and whup on him bad. They might never kill Thanos, but The Doctor could definitely "win" the fight.
Problem is, he's never written to potential since it would make some story arcs boring...though they've been creative with giving reasons for him not intervening (comatose from an overdose, doesn't agree with The Authority, loses his powers to an evil Doctor, is just learning to use his powers, etc.). But if they ever decide to write him to full potential I have a feeling a Doctor vs. Odin/Galactus/Abstracts/teams of magic-people, etc. thread wouldn't be out of the question (just one-on-one though, not at the same time).
-DM