This is a project for Lego, not Arduino.
I've been nerd sniped thinking about this. Latest thinking: simple sliding bar clamp to hold two edges of the PCB. The PCB hangs down into the solvent tank. The bar on the clamp drops into vees at both ends. One end of the bar is bumped with a motorized cam, the other has a spring. The clamp+PCB oscillates back and forth and the arms agitate the fluid. When the cycle is complete you just lift the clamp+PCB out of the tank. The tank doesn't move. Tank shape can be optimized to minimize working fluid and agitation.