I checked this out and this run seems pretty solid. One very noticeable improvement that I know of is that both of the final boss forms can be sped up considerably by shoving the boss to the left corner and getting double stabs per boss pushback. This also prevents the boss from attacking and having to deal with the jump height RNG. I know of this from the RTA runs and from the Sega Ages Switch replays. I also don't know how much of an RNG challenge it would be to get gauntlets before as many bosses as possible could save time but it's worth looking into. The last idea I can think of is only buying the best boots and getting the sword upgrades. While not getting armor reduces the amount of potential damage boosting in a run it does simplify the money route.
Those all sound like great improvements! If I can find the time someday maybe I'll take another stab at this one. I definitely put it together hurriedly.