I've been replacing a lot of tub drains, just the metal part from the tub side. They can be a pain to get started and not cross threaded and it's hard to see if you are holding it level. So I made a level by gluing (super glue gel) a bulls eye circular level onto a 3/8 x 1 1/2 bolt. The drains I use have this size threaded hole in the center. I screw the leveling bolt into the drain and then it's easy to keep it level while starting the threads. Hardware store probably has everything for under five bucks.
Mark