My guess for King of Monsters (following on from previous Elwin games) is that not only will you have to battle against all monsters, but actually defeat them as well.and King of the Monsters, which I assume will be qualified by doing Planet x, Monster Zero and Terror of Mecha but that's just a guess. I don't know if King Caesar is just art work, there's a couple of other names on there too with no modes
Or it could be even harder that you have to get a SJP in both Train and Tank MB and complete Power Strike in EACH city, along with defeating each monster as well as completing Planet X - that would follow the likes of RTTH and WDRTE as ultimate wizard modes.
Time will tell.