What is the secret move I need to use on Cockroach King?

[Sextilidan]

Guy on ship says there's some sort of reward if I defeat the training boss with special move.
Also how does STR affect the damage formula?
Is 1 STR = 1 ATK?
Is 1 STR = 1% DMG increase?
What is the actual damage calculation?

[The nameless Gamer]

Probably down-up and artifact 1, the special.
Str is, AFAIK, 1 ATK.
The damage calculations are not as simple. There are two types of damage: physical and magic. Most weapons do physical damage, but your ultimate attacks as well as "artifacts" (such as the Light Arrow spell you gain in the tutorial) have magic damage, which is calculated from INT. However, much like your character(s), enemies also have two types of defense: DEF against physical attacks and MND against magic attacks.

[RabidHobbit]

This game isn't super popular, so I doubt anyone knows the damage formula.

ARP is armor piercing, so we know enemies have armor, which means 1 STR cannot possibly mean a direct 1% increase.

You can see each weapon and ability's final attack rating in the stats screen. I assume that plus ARP and MRP (or whatever magic piercing is called) are the best stats to figure out how much damage you'll do.