No, not greenboard. I am fairly certain that you want a cement board-type wallboard; Hardibacker or Durock are two biggies (DH used Hardibacker--got it at Home Depot). You also want some sort of waterproofing. Either the Kerdi system (a fabric-like membrane) or a roll-on (Hydroban or Redguard for ex.). None are cheap but well worth the protection.

If it's a rental, I'd be sure to install a switch for the fan that has it turn on every time the light is turned on. You can put in an exhaust fan, but if your tenants don't use it, you'll continue to have problems. I wouldn't need to do that in my own home, because I have incentive to use the fan, but not sure all tenants would be that careful.

Green board would be fine behind and above a tub surround. Make sure the outside wall is well insulated. Install the exhaust fan and prime and paint the walls with a good enamel paint.