re: Issue with apartment complex over AC unit

If it's not in writing from you, the problem does not exist, legally.

Document it all. Send in certified mail to the landlord. Ask for rent concessions in that letter to make you whole in what you paid for by renting.

Most likely in your lease, you agreed not to offset the rent by paying for maintenance and you will be in default if so and liable for possible accelerated rent through the end of the term.