Reaching a different rank in the Monster Arena will earn you an item and a special award from Morrie. Here is a list of all the prizes you get for reaching the different ranks.
"Bardiche of Binding" --> Reach Rank B
"Bunny Suit" --> Reach Rank F
"Dragon Robe" --> Reach Rank S
"Hero Spear" --> Reach Rank A
"Mighty Armlet" --> Reach Rank D
"Ring of Clarity" --> Reach Rank E
"Saint's Ashes" --> Reach Rank C
"Strength Ring" --> Reach Rank G
Call Team Ability For Hero --> Reach Rank E
Hero Statue --> Reach Rank S
No Entry Fees --> Reach Rank S
Option To Fight Against Your Team --> Reach Rank F
Second Monster Team --> Reach Rank B
Three Additional Reserve Monster Slots --> Reach Rank D
Three Additional Reserve Monster Slots --> Reach Rank G
Unlock Rank S --> Reach Rank A