Is there any responsibility of the landlord, as far as utilities being capable of cooling, and insulation?

No.....if the temps are at 77 degrees there isn't a habitability issue. I'd go out and purchase a portable window A/C unit and move when the lease is up.

If you are saying it's 100 degrees outdoors then you need to take other steps to cool the place, but believe me it will be impossible for you to get it lower than 77. I live in FL and can tell you as the years go by even if you live in the same apartment for a long time that the weather has been getting hotter. Every year I get my AC checked out 2 or 3 times, change the filters twice a year, and have them clean out the pipes and put in freeon, when it's 92 outside then it's 85 inside and there's no way I can bring it down past 85. Indoors has been 85 for a couple of months now. It's when it's humid outdoors that's the worst and I use 3 fans plus the AC during that time. I also handwash some clothes and hang them over the tub on a pole and that seems to make things a tad bit cooler. The electrician verifies that the AC unit is the size it should be for my efficiency apartment.

I do know that the top floors are hotter than the first floor so you might want to ask the renters on the first floor if their place is cooler than yours, and if so then if you've lived in the place for a year you might want to ask the lanlord to put you on the list for a first floor apartment the next time one comes available. My electric bill is $35 a month and goes up to $50 when it gets hot in summer. Once when I didn't feel well and almost froze up the AC it cost me $60. So if yours is costing you a mint then you might want to use insulated draperies and plastic, put insulation around the windows and door, anytime that the nights seem somewhat cool then unplug everything (like turn off the AC and all fans).

If you unplug everything (that gets plugged into the outlets) then that will save you money too, as will not using the dishwasher, the washer and dryer. You can do those dishes by hand, and get your laundry done in the public laundry room.

The landlord is not required to supply AC as it is only considered a necessity in certain areas of AZ. He has provided you with a working AC unit; it does not have to be energy efficient.

You might try changing the filter. And be sure that the cold air return is not blocked. Use fans to help circulate the air. Keep your curtains and blinds closed.

NOPE. AC is not legally required to be included in any state but AZ. They are not legally required to make it energy efficient or even to make it work properly . They would not be braking any laws if they did nothing with it at all. It may not seem fair in other hot states like TX but that is the way the law is written.