Is there any card for support destroyer at the white deck or just luck and Sword of the animist ? 
Doesn’t look like it, but you could also use cards like gem-converting supports to set up matches which let you get rid of supports faster.
That’s the only solution I can think of, apart from using a creature like Knight of the White Orchid, which transforms gems to White upon entering the field.
feniold Cub, or whatever it’s called. active to Destroy’s supports and itself.
The only colors that has true support removal are white (which is rather lousy at this point since it’s only the Cub and it must sacrifice itself to do so - AND it’s bugged for now!), red, and green. Red has a plethora of anti-support cards, two of which are rather obvious and many cards have gem destroying effects that can potentially target support gems indirectly. Green has the second best options - one being a 8 mana spell, and a 4/4 creature for 11 mana that destroys a support when played (there’s also mass gem conversion methods… but that usually requires supports of your own).
Yes, I had to use Felidar Cub in several story encounters where the opponent had several powerful supports (e.g. Oblivion Sower, Heroic Gideon (the Starfield of Nyx version), and Heroic Jace (with Thopter Spy Network). Even so, these encounters took several tries to beat!
Actually story modes are meant to need proper deck building to overcome.
This means also switching planeswalker to get better chances even more if you are after crystal achievements.
For pvp balance purposes well… Not everyone can have everything.
This is particularly true for mono colored planeswalkers.
In paper magic you can build multicolored decks to overcome a color weakness.
Here we have multicolored planeswalkers.
@Morphis: The color challenge requires us to beat the encounter with all colors. The multicolor PWs help, but the cards are still limited.