What size Wire and breaker for Mitsubishi Mini Split HVAC
The problem is your attic temperature

Phoenix makes outside-the-insulation-envelope attics just stupidly hot, and so you run into trouble at NEC 310.15(B)(2)(a) - the thermal derate.

Suppose we use 12 AWG wire that is allowed 90C for thermal derate purposes (NM-B or UF-B).  The 90C column in 310.15(B)(16) gives you 30A "to play with". When you derate that to 50%, you find yourself at 15 amps.  Well, look at that. That's enough.  And that 50% derate will cover you all the way to 167F, according to 310.15(B)(2)(a).  Which hopefully will be enough.  

If we need 176F we'll need 10 AWG wire; if we need 185F we'll need 8 AWG wire.  

You may want to discuss with your inspector what they expect. 

Now, the circuit breaker must be 15A, because the UL-approved instructions say so.  

Now it looks like this unit will pull less than 7.5 amps normally. That's less than half of circuit capacity, so you have the option to run a neutral wire and install a service receptacle as ThreePhaseEel describes, and for those reasons.