Here is the full list of all 11 Brotherhood United achievements.
Pass through a mission without using grenades. Cool guys don't look at explosions
Reach the end of the first mission
Rapid fire your old good gun
Joined the road crew
Get all the stars in all missions. Reach for the stars
Pass through 4 missions without game over. There are 2 kinds of people in this world, those who think die hard is a christmas movie, and those who are wrong
Game over more than 3 times on the same mission. Welcome to the party pal
Get 3 stars on any mission
Beat the game
Don't let the B1 be destroyed on B1 rampage mission
Finish Brotherhood United in COOP mode