There are a total of 13 unique skills that can be acquired only in multiplayer. All of these skills are unlocked through various trials. You do not need to unlock each skill, only a total of 10 points out of a possible 19 (some skills have multiple ranks). You will acquire this achievement on the way towards unlocking all trials, and likely all of the multiplayer-only blueprints.
In order to unlock enough skills for the achievement, you will need to complete most but not all of following trials:
Bling III - Create 10 Gold Combo Weapons
Epic Loot III - Kill 25 Loot Zombies
Day Tripper III - Complete 25 Days in Multiplayer
Helping Hand II - Revive another player 10 times
Looter IV - Collect 100,000 Scrap from zombies
Counting Calories - Survive a day without anyone dying or eating food
Pacifist - Survive a day and complete a mission without anyone killing a zombie
I Get Knocked Down - Finish a day where every player is revived once, but no one dies
Zombie Killer MVP III - Earn the Zombie Killer MVP title (by killing the most zombies in a single day) 10 times
Speed Demon - Be the first to arrive at the Safehouse 25 times