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