To earn the Squad Goals achievement in Ghost Recon Breakpoint, you have to first adjust your matchmaking settings. Go into the pause menu and scroll left of the map and select JOIN PUBLIC MATCHMAKING. Otherwise, you'll be stuck in solo mode.
From there you'll be playing online, though maybe still solo momentarily. Allow others to come into your game or join theirs when the game prompts you. At that point, you can play any three types of missions. They need not be the main story missions. Faction missions and Auroa Archipelago side missions count too, though weapon objectives appear not to count.
You can also easily invite friends or join games of others in the social hub, Erewhon. The achievement will unlock as soon as your third mission is completed.