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You may want to call the city to see if the landlord is in compliance
with codes, or if there are no codes, see if there are any incentives
available to you or the landlord for dealing with efficient cooling.

In general, you will want good shades over any south-facing and east-
facing windows. Keep the number of open windows to a minimum, have
one with a fan that blows out (on the south or east side) and one with
a fan that blows in (on the north or west side). Then you will at
least have a current of the coolest possible air. It's not really a
solution, but it may help some.