Here is the full list of all 48 Family Guy: Back to the Multiverse achievements worth 1,000 gamerscore.
You completed the "Handicapable" level
You completed the "Something's Amish" level
You burned the Amish pot fields
You've killed 75 enemies with headshots
You successfully performed a multi-kill with a melee weapon
Your team won an Infiltration map
You've successfully completed a taunt 25 times
You taunted 5 times in a row with Peter
You killed yourself with a grenade or satchel charge
You've shut out the other team from scoring in Capture the Greased-Up Deaf Guy
Your team won a Capture the "Greased-Up Deaf Guy" match
You taunted a dead opponent with Quagmire in Multiplayer
You completed the "It's All Greek To Me" level
You've switched between Brian and Stewie 10 times
You have won a Deathmatch mode (free-for-all or as a team)
You got a 10 kill streak in Deathmatch
You've meleed 3 members of the opposing team in Multiplayer
You completed your first kill of a member of the opposing team in Multiplayer
You killed Meg during a Multiplayer Match
You selected Meg as a character for a Multiplayer Match
You defeated 10 enemies with a melee weapon
You successfully performed a multi-kill with a grenade
You got your first head shot
You've killed an enemy with one shot
You've destroyed all of the piñatas
Unlock all other Achievements found in the game
Complete the "Pussy Whipped" level
Complete the "No Cheese, Please" level
Complete the "Long John Peter" level
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
Collect $50,000 in Story Mode
Kill 60 enemies with grenades/explosives
Acquire any collectible special inventory items and use it 25 times in Story Mode
Buy everything available in the Store
Kill 500 enemies using Stewie
Kill 500 enemies using Brian
Earn 10 stars in Challenge mode
Earn 21 stars in Challenge mode
Play poorly during the final showdown
Survive 30 waves in Multiverse Madness
Survive 15 waves in Multiverse Madness
Smash your opponent into something 20 times in the "Chicken Fight!" level
Hang around the room with Quagmire in a baby costume for 30 seconds
Kill Vernon