Sure it is doable. Little ones all over the place many working out of homes or small cement block buildings. Much cheaper than USA. Best to speak Spanish or go with someone who does. Can find guys who are really good at it. Just like mechanics , radiator repairs, mufflers etc.
Have to keep your eyes open for the signs to find them.
Taller is mechanic shop but you will just see a sign A/C or Aire acondicionado. These shops can be well hidden down a side street or behind someone’s house.
Or you can go to a bigger all-purpose place like in the states. They will still be cheaper than USA and maybe easier to deal with. I prefer the small guys who work behind their houses myself. Referred by a Mexican friend is best
I tell you trying to do all this without any Spanish can be done but it is difficult talking about details. You can write it out in English then google translate and then print it. But then the question and answer part is difficult. Yes you can take a translator as well. That would work.
Good Luck. Also some car brands are better than others for parts.
We are very fortunate that we have an auto mechanic who is not only very honest, but speaks impeccable English. I can't call him a 'friend' - but we are friendly. He has been to our house and we have been to his. We are in the middle of Mexico - but if he needs a part for our car he can get it here in a couple days. I generally prefer his ordering the parts because if it arrives and is wrong or crappy he sends it back - and I guess he does enough business with them that he has some clout.
What we have found in Mexico is that people are much more prone to fix something than replace it. Our car's A/C got into a state where it would only throw air at the windshield (defrost) and not out the feet vents / dash vents. The mechanic pulled the dash and found that the box which holds the flapper which directs airflow was cracked and the flapper was not flapping. So - they repaired the box. A couple years back our rear end was a little 'bouncy'. We took the car to a shop referred by the mechanic and rather than replace the 'sleeves' (which would have been big $) - they took it apart and inserted a new more rigid sleeve into the mix. And to boot - we received a verbal quote on the project at something like 800 pesos. Well 4-6 hours later (and the job being much larger than they had assumed) - he would not accept a penny more than 800 pesos even though what was supposed to be a one man / one hour job turned into a two man job (albeit family).
Mexico can do amazing things with vehicle repair, high pressure hoses can be rebuilt, compressors can be rebuilt... pretty much anything can be rebuilt, at a fraction of the "replacement" costs we have grown so accustomed to in the US.
If you're planning on staying for a bit, I'd recommend you look for a solid "general mechanic" shop, were you'll do most of your wrenching, and ask them to recommend you go a solid AC repair shop.
Sometimes folks will wrench a little bit on everything, but will not really know the ins-and-outs in a particularly mechanical discipline.
I'd rather take my vehicle for "specialists" treatment, for certain things... i.e., transmission, electrics, and AC.
Everything else is handled by my general mechanic, or "mecanico general."