I am framing a shower up and am attempting to create a sturdy wall on which I plan to use a shower membrane and then wall tile. Three of the walls are strong enough already, but the fourth wall needs some extra strength. I do not have a ton of room, so keeping the wall as thin as possible is beneficial. The wall is being framed just inside from an exterior brick wall. What are some good ideas for shoring up this wall?

How tall is it? If it is normal 8-foot height, then there is nothing wrong with good old 2x4's 16 inches on center. For additional stiffness, use 3/4 inch fiberglass-Portland cement board on the tile side.