I have been a renter in a duplex apartment for several years, and I am unfortunately having some trouble with my upstairs shower. It has been clear for some time that the shower unit has been in need of repair, but recently water has begun leaking through to the first floor bath and it is obvious that the backer board behind the tile near the shower faucet has become soggy - tiles near the bottom are beginning to detach and it seems a large section of the tile wall is in danger of failing completely.

What would be the minimum expedient repair required to prevent further damage and allow the shower to be usable (until the inevitable renovation that will take place when the unit is vacated)? 

I live in the Northeast U.S.