The Arizona Landlord/Tenant Act applies to the rental of dwelling units like apartments and houses.  Under the Act, a landlord is required to provide essential services.  According to Arizona Revised Statutes, Section 33-1364, hot water is considered one of those essential services.  However, forcing the landlord to repair the problem requires that you take all the correct steps.  First:  you must notify the landlord in writing that (a) the hot water is not working; (b) that he has 5 business days to fix the problem; and (c) if it is not fixed within the time period, you will terminate the lease and move out and sue for damages caused by the need to move.  Second: once you have written out the notice, you must "serve" it on the landlord.  You can either hand-deliver the notice or mail it certified mail -- return receipt requested.  If you elect to hand deliver, either video record the delivery or take an impartial witness with you.

If I have misunderstood your question and you do have hot water, just not in the shower, then the landlord would have 10 days to fix the problem.  If it is a small problem like the hot water faucet not working, there are other options. You can fix the faucet yourself and deduct the cost of a new faucet from the rent.  However, the cost of repair must not exceed $300 or half the rent. (33-1363)  Once again, you must follow the written and served notice requirement.