Use Easy Off No Fume oven cleaner in the BLUE can. Spray it on, let it liquefy, rinse well.
Fill a spray bottle with a 50/50 solution of Dawn dish soap and vinegar. Spray it on the tub and let it work. You may have to do a little scrubbing, but this solution will cut through hard water stains and soap scum.
The recipe I use use is in a 32 oz empty plastic bottle, add 5-6 oz blue dawn dishsoap and fill to the top with white vinegar, give this a mix. Cut or poke holes in the cap and spritz around the areas of the tub/shower that are dingy/scummy and let it soak. Take a new dedicated broom from Dollar Tree (blue bristles and a white handle) and clean your tub. Rinse, repeat as often as needed. This new broom is for this use only because you don't want any scratches from the floor debris.
I recommend using dawn dish soap and hydrogen peroxide, peroxide is an oxygenated bleach that is very effective at lightening discoloration