Below you will find a chart which tells you about the general weakness of different elements of monsters.
Below you will the above table represented in short:
Weakness Chart
As you can see, each element of monster has a weakness against another, so you must remember these when you are fighting other players in the monster arena. Each monster also has a unique skill that you can use in the battles, so use it wisely. The player which uses the skills wisely usually wins the battle.