Some good products for properly cleaning an acrylic bathtub are dish detergent, baking soda and a soft sponge. Avoid chemical solvents that break down the acrylic and scouring pads that scratch acrylic surfaces.
Fill the tub with a few drops of dish detergent and warm water, and then let it soak for 30 minutes. Drain the tub, and wipe it clean with a soft sponge. If soap scum remains, use a small amount of baking soda on the sponge and gently scrub in a circular motion. Rinse the surfaces with warm water and dish detergent to remove the baking powder. Polish the surface with car polish to protect the finish between cleanings.