Here is the full list of all 48 Family Guy: Back to the Multiverse trophies - there are 38 bronze, 7 silver, 2 gold and 1 platinum.
Unlock all other trophies
Survive 30 waves in Multiverse Madness
Earn 21 stars in Challenge mode
Survive 15 waves in Multiverse Madness
Earn 10 stars in Challenge mode
Buy everything available in Store
Complete all secondary objectives
Kill 60 enemies with grenades/explosives
Kill 500 enemies using Stewie
Use the collectible special inventory items 25 times in Story Mode
Win an Infiltration map
Shut out the other team from scoring in Capture the Greased-Up Deaf Guy
Win a Capture the "Greased-Up Deaf Guy" match
Taunt a dead opponent with Quagmire in Multiplayer
Taunt 25 times in any Multiplayer match
Taunt 5 times in a row with Peter
Win a Deathmatch mode (free-for-all or as a team)
Get a 10 kill streak in Deathmatch
Kill 3 members of the opposing team with a melee attack before you die in Multiplayer
Successfully complete your first kill of an opposing team member in Multiplayer
Kill Meg during any Multiplayer Match
Choose Meg for a Multiplayer match
Complete the "No Place Like Home" level
Play poorly during the final showdown
Complete the "Chicken Fight!" level
Smash your opponent into something 20 times in the "Chicken Fight!" level
Complete the "Chickens In Space" level
Complete the "Santa's Sweatshop" level
Kill Vernon
Collect $50,000 in Story Mode
Complete the "Long John Peter" level
Kill 500 enemies using Brian
Defeat 10 enemies with a melee weapon
Complete the "No Cheese, Please" level
Hang around the room with Quagmire in a baby costume for 30 seconds
Complete the "Pussy Whipped" level
Kill yourself with a grenade or satchel charge
Perform a multi-kill with a grenade
Complete the "Handicapable" level
Complete the "Something's Amish" level
Burn the pot fields in 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 melee weapon
Switch between Brian and Stewie 10 times in Story Mode
Kill an enemy with a single shot to the head
Successfully kill an enemy with one shot
Destroy all of the piñatas in the "It's All Greek to Me" level