First of all, make sure your computer meets the minimum system requirements (see above). Some things that might help to improve performance, are lowering the graphical details. Also, running the game in a lower (800x600) resolution might work. At the time of writing it's unsure if this can be chosen from a menu or has to be done manually. See the official
BodyShop Help page for some tips (scroll to the bottom). You can also use the "vsync off" cheat to improve performance. Press and hold Control and shift, then press C and release the buttons. Type "vsync off" (or "vsync -off", at the time of writing the exact cheats haven't been confirmed yet, type them without quotes) and press return. The game should run somewhat faster, but graphical errors may be a side-effect