I have beaten Medusa before without first getting the Mirror Shield. That's absolutely doable.
What I am wondering is this: would it be possible to beat Medusa as soon as you get Noah? I mean, you could still grind, but no equipment upgrades. So, your equipment would look like this:
Alis:
CRC.SWD
ZIR.ARMR (or DMD.ARMR)
CRC.SLD
Myau:
IRN.FANG
THCK.FUR
Odin:
NEEDLGUN
ZIR.ARMR
CRC.SLD
Noah:
SHT.SWD
WHT.MANT
It would be extremely difficult to get to the top of the tower (even at a high level) with that equipment. The lack of defense would not matter at all in the battle with Medusa, since you get one hit KO'd anyway. The lack of the LASR.GUN would hurt big time, though. Noah's WIND would be your heavy hitter. Alis would be using ROPE every turn.
You need favorable RNG to even do it with good equipment (sans ths MIRR.SLD of course). Could it be done with the inferior equipment? If so, what's the lowsst level it could be done?