It is possible to beat the fight without using Mix at all (either use Aegis Shield to deal with Tidal Wave, freeing your Accessory slot for a Flame Ring to negate Ice and absorb Fire, then use a Potion if you're low on health in order to be able to survive Lightning, or simply use the Force Shield, which will allow you to use Hermes Boots, saving you a turn on casting Haste on yourself, in addition to granting you immunity against every element Shin can use), but didn't feel like extending this fight for too long. Dealing less damage is one thing, but not being able to apply the 'Heavy' flag on yourself will extend the fight considerably, both for the Maelstrom animation playing out in the first place (multiple times), and if your HP drops below a certain threshold, and if you learned the ability, your character will start to use Magic Shell in place of a counter-attack, significantly lowering your damage potential.
Was very lucky that Shin didn't use Mighty Guard at all. Idea was to buff to max level to be able to deal as much damage as possible when Shin casts Mighty Guard, but that ended up being not necessary, so I just proceeded to attack him once I hit the damage cap.
Used Samson's Might in place of Dragon Power throughout the fight in order to avoid having a level that's a multiple of 3, or else Lv 3 Flare would have ended the run.
The reason for using Guard (deliberately delaying it until after Shin did an action) instead of Mix in the second Atomic Fire / Ice Storm / Lightning loop was a safety measure to prevent Shin from eventually getting a turn in the exact moment when I get mine (if this happens, your character will no longer be in Guard stance, which means Shin can defeat you right there if he decides to use a physical attack).