Machamp Solo Team

Look at your recommended list and choose your team based on it. If there's flying types in your recommended, you can assume its not rock slide.

Rock Slide: Espeon, Mewtwo, Alazakam, maybe gengar, maybe exeggutor

Non Rock Slide: Lugia, Flying types, high DPS options such as Espeon, Alakazam, Mewtwo

For the psychics you're going to want Confusion over Psycho Cut/Zen Headbutt for maximum efficiency. It's difficult to dodge with but the damage difference is enough to compensate in most cases. All have optimal charge moves, including Mewtwo being shackled with Psychic. Moltres > Dragonite as it resists its steel moves in addition to its fighting ones, plus Sky Attack is a much better move than Hurricane. Rock Slide will continue to give you trouble - I haven't solo'ed one with it yet so I don't have firsthand experience to speak of about it.

You can definitely solo all movesets with that team, if you dodge some charge moves. Without dodging it's a different story.

Metagross as mentioned is the best TDO counter against Rock Slide. C/P Gallade is another good one as it resists RS. If you have a Lugia, it's still one of the best TDO counters even against Rock Slide.