Elicon's Level Up Ability is used best in a situation when the player is mimicking their opponent's treasure values as best as they can, thus causing a build up of Heroes in town. Upon activation, all Rooms in the dungeon have their Treasure Value doubled, which would then lure in every Hero in town. This is a risky move, however, as it can mean either the player's victory, or their doom. Especially if Item Cards are being used.
Elicon's Ability is also good to use when in a Treasure stalemate with an opponent over one particular Treasure, and can assure the player can break the stalemate.