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This is a mostly good guide, but to clarify:

Pre-fight: Use the Return Bell to escape back to town. Talk to Mandrake again and you can find an Adamantite Charm in the room of Mandrake plushies. You can buy two more from the Altomyostr merchant for 150 honor medals each. I also recommend purchasing the Resuscitation skill for everyone, Ran's Whisper of Sand skill, and Elucia's Aegis Protection skill from the nun.

Phase 1 (horse form): You are largely dependent on Elucia's Shield Bash to inflict a stun effect every turn. Ran's Whisper of Sand skill can help regenerate Elucia's MP. Since you have minimal HP, Marie's Magic Syntax does a lot of damage. Once he falls below half health, he will steal your shields and buffs, so stun lock as much as possible.

Phase 2 (rhino form): Keep your shields up above all. You have the chance to heal in this phase but one of his attacks inflicts a heal-block debuff. It is the only debuff in this phase so Soothing Salve can take care of it for everyone at once. He attacks more often in this phase but as long as your shields are up then the Adamantite Charms will deal reflect damage to him as he tries to break through. Focus on keeping everyone's MP charged and gradually healing.

Phase 3 (slime form): Don't Panic. Wait for the cutscene. You'll be fine.

You can lower the difficulty by picking up the item left in the magic circle where you first meet Goddess Lavia.
Doesn't seem to affect this boss fight at all.

Very well constructed, clear objectives and methods to achieve it, and the jam's theme of "Progression" is present in the map, art, gameplay, and story.
A near perfect entry for this game jam.

Nicely done.
I see you're aware of the credit scaling issue (personally I had more than I could spend by the end of cycle 4). As a suggestion, if you increase the price for each successive upgrade (even just by 1 credit at a time) that should flatten out the growth curve a lot.