Ok, first of all, Zero Suit beats Link in the air and in nuetral. Her punish game as well as her combo game is very good. Link will probably have to focus on avoiding paralyzer shots and zoning Zero Suit out, which is pretty difficult considering her excellent mobility options.
Zero Suit's Assets:
>Paralyzer Shot and Down Smash have huge payoffs
>Down Special can bury opponents and at higher percents, leads into a guarenteed Up Special
>Down Special also can also meteor airborne opponents as well as kill if Zero Suit intiates the kick
>Zero Suit has good ground speed and one the highest jumps in the game
>Three reliable recovery options, zair/side special tethers, down special, and up special
>Jab and Utilt come out very fast, Jab might be frame 2
>Usmash has excellent aerial coverage
>Tether grab, although slow, stays out for a longer time than normal grabs, meaning Zero Suit can occasionally catch rolls and spot dodges
>Down throw true combos into Uair, Fair, or Bair
>Uair is a great juggling tool and strings into itself similar to Captain Falcon's uair
>Bair hits high, but does the most knockback out of all of Zero Suits aerials, one of her kill moves
>Fair hits twice, second kick is capable of killing while the first is not
>Nair is decently strong dealing 10%
>Dair is the standard stall and fall kick, meteors in the beginning of the attack
>Up Special is Zero Suits best kill move, as it can be comboed into Uair strings and kill rediculously early
>Simon Belmont Zair is arguably better than Link's, as it comes out decently fast and pairs better with Zero Suits mobility