Check the plumb of the wall with one of your levels (the longest one) to determine how bad it is out of plumb and where you need to shim it out. The largest swell in the wall studs is what you need to match everything else to. Move your level around in various angles and directions (along the studs, diagonally across them, perpendicular to them) to check all the studs in regards to the high point.
Shim out the wall studs according to how much you need to match the largest swell in the studs. Line the stud with however many cardboard strip shims are required to match the low points to the high point in the wall. You want everything plumb up and down as well as flat across the entire length of the wall from side to side. Staple them to the studs with the hammer tacker.
Double-check your studs by placing the level across the shimmed areas to ensure everything is plumb up and down and flat from side to side. Screw the backer board on the wall on top of the shims and set your tile. Ensure that your screws are long enough to sink through the cardboard shims as well as the underlayment and give you at least an inch of depth into the wall stud.