I beat Mega Man X4 damageless following a set of rules:
Single Segment
No Glitches/Skips
No Ultimate Armor
No Ride Armors
No Pausing
No Charged Soul Body
Although not ruled out, I also didn't go for the helmet or body armor parts, beating the game only with arm and leg upgrades.
This run was done on BizHawk emulator in real time through my stream at: / raindropdry
The reason this was done on BizHawk is to avoid any and all QoL improvements that the Legacy Collection version would have otherwise added.
This run was largely inspired by @cleartonic, who beat every classic Mega Man game (as well as Mega Man X1) damageless following a similar ruleset.