The difficult part of this achievement is earning a new character and some weapon skins by buying card packs from the store. You'll need to play Horde or Versus modes to earn enough credits to do this. It will take a few tries before you earn a character, which are automatically Epic or Legendary level cards (and so quite rare). If you have 600 scrap (by destroying other cards), you could also craft a character from the customization screen.
Once you have a character card with a yellow or purple border, select this character in the customization menu and apply skins to your two starting weapons. For example, I got this by switching to E-Day Anya (who I'd won in a versus booster pack) and applied the Urban Lancer and Sky Camo Gnasher.
From there, go out to Versus, pick your favourite game mode and win the match. It's usually quite easy to win a Co-op vs AI match, so I did that. When the final score is shown, the achievement will pop.