This is simply defeating Dark Link, who is simply a recolour of Link.
The title of this Event Match most likely is a reference to Zelda II: Adventure of Link, which featured a final battle against Dark Link as well.
The description of the event is "Everybody has a dark side. Link has two!". The word "two" could be a reference to Zelda II, the fact that Dark Link had appeared in two games at the time (Zelda II and Ocarina of Time), or to the fact that Dark Link has two lives in the event match. It could also be a typo and the intended meaning was "too". However, this would grammatically be incorrect if it was indeed a typo. It may even a reference to the fact that both links have 2 lives.
Link is in his red color swap in this event which is a homage to Zelda II's Shield Spell.