This card's effect is actually much more desirable than that of the two Fusion Monsters that this card fuses into, because you are able to choose which opponent's card gets destroyed, and they will also take damage. If your opponent has a "problem card" waiting for you in their hand, like "Neo-Spacian Grand Mole" or "Forbidden One" parts, you can get rid of them before they become a problem.
If you control no monster(s) with ATK greater than a Monster Card in your opponent's hand, you can make use of the effect of "Damage Mage" to regain what you lost due to the effect of "Aqua Dolphin" and Special Summon this card to the field. From there, you can make an easy Xyz Summon of a Rank 3 monster.
One desirable side effect of this monster is that you can view your opponent's hand. By using this card in combination with "Mind Crush" or "D.D. Designator", you can get rid of two cards in your opponent's hand.
This card works well in "Atlantean" and "Mermail" Decks, as it can activate many of their effects when it discards them for its cost.
Since this card's discard requirement is a cost, you can discard a monster with high ATK to first activate the effect, then Chain "Call of the Haunted" or something similar to Summon the same monster from your Graveyard, thus ensuring you have a monster with an ATK greater than any monster in your opponent's hand.
When activating this effect, it's a good idea to discard cards that activate when sent to the Graveyard, regardless how they are sent. For example, discard "Skull-Mark Ladybug" to gain 1000 Life Points, "Dandylion" to generate "Fluff Tokens" (though it does put the Tokens at risk, so be wary), or "Archfiend of Gilfer" to weaken an opposing monster by 500 points.
Equip this card with "Mist Body" or "Heart of Clear Water" to protect it from being destroyed in battle so you can reuse its effect come next turn.