As the raid graph for Machamp shows, the best counters have about 20% total damage output, meaning you will need five good attackers to successfully solo him. This is my experience, too. With two Mewtwos, one Alakazam, and one Exeggcutor you will need at least one more. Machamp Solo Raid Guide lists all options.
GamePress
Solo Machamp Raids
I am currently Level 29 and I have around only 5 ( I know right ) mewtwos all between 2200 and 2300 cp ( all psychic movesets ). I have a zam at 2480 cp and an exeggcutor at 2000cp with extrasensory and psychic.
I am holding off for Espeon because I have no high IV/CP eevees though I have 500 eevee candies :)
Am I close to soloing a machamp and if the answer is no, what mons should I evolve/power up/get?
BTW my trainer code is 1118 0347 6643