Switching 15 amp breaker to 20 amp for AC unit
Yes you can swap breakers out, but take extreme care to match wire to breaker.  Don't use 14 gauge (generally white) wires for a 20 amp circuit.  Also note that most 220V circuits in the USA require a tandem breaker taking two slots.

Investing in an electrical permit is highly recommended, if your jurisdiction will inspect at the end of the job.