Here is the full list of all 48 Family Guy™: Back to the Multiverse achievements.
Successfully collect $50,000
Acquire any collectible special inventory items and use it 25 times in Story Mode
Win an Infiltration map
Successfully perform a taunt 25 times
Taunt a dead opponent with Quagmire in Multiplayer
Win a Capture the "Greased-Up Deaf Guy" match
Shut out the other team from scoring in Capture the "Greased-Up Deaf Guy"
Taunt 5 times in a row with Peter
Win a deathmatch mode (free-for-all or as a team)
Kill 3 members of the opposing team with a melee attack before you die in Multiplayer
Play poorly during the final showdown
Complete the "No Place Like Home" level
Complete the "Chicken Fight!" level
Smash your opponent into something 20 times in the "Chicken Fight!" level
Complete the "Santa's Sweatshop" level
Complete the "Chickens In Space" level
Kill 60 enemies with grenades/explosives
Kill 500 enemies using Stewie
Kill Vernon
Kill 500 enemies using Brian
Complete the "Long John Peter" level
Complete the "No Cheese, Please" level
Hang around Quagmire in a baby costume for 30 seconds
Kill yourself with a grenade or satchel charge
Complete the "Pussy Whipped" level
Complete the "Handicapable" level
Perform a multi-kill with a grenade
Select Meg as a character for a Multiplayer match
Get a 10 kill streak in Deathmatch
Successfully complete your first kill of a member of the opposing team in Multiplayer
Kill Meg during a Multiplayer Match
Complete the "Something's Amish" level
Burn the Amish pot fields
Kill 75 enemies with headshots
Complete the "It's All Greek To Me" level
Switch between Brian and Stewie 10 times in Story mode
Defeat 10 enemies with a melee weapon
Perform a multi-kill with a melee weapon
Kill an enemy with a single shot to the head
Successfully kill an enemy with one shot
Destroy all of the piñatas
Complete all secondary objectives
Unlock all other Achievements found in the game
Earn 10 stars in challenge mode
Earn all 21 stars in challenge mode
Survive 30 waves in Multiverse Madness
Survive 15 waves of enemies in Multiverse Madness
Buy everything available in the Store