Here is the full list of all 48 Homefront trophies - there are 36 bronze, 8 silver, 3 gold and 1 platinum.
Complete chapter 6 in the Single Player Campaign without dying or restarting a checkpoint
Hijack the tankers in less than 8 minutes in one life in Chapter 6: Overwatch
Complete chapter 7 in the Single Player Campaign
Destroy all vehicles using the UAV in Chapter 7: Golden Gate
Jump off the Golden Gate Bridge in Chapter 7: Golden Gate
Complete chapter 6 in the Single Player Campaign
Destroy all the SAM trucks in the level in Chapter 6: Overwatch
Complete chapter 5 in the Single Player Campaign
From the front door of the church, make it to the crow’s nest in 240 seconds in Chapter 5: Heartland
Complete chapter 4 in the Single Player Campaign
Kill 5 enemies while they are on fire in Chapter 3: Fire Sale
Complete chapter 3 in the Single Player Campaign
Don't kill any of the enemies that are on fire in Chapter 3: Fire Sale
Complete chapter 2 in the Single Player Campaign
Destroy the first sentry without taking any damage in Chapter 2: Freedom
Talk at least once to each inhabitant of Oasis in Chapter 2: Freedom
Complete chapter 1 in the Single Player Campaign without dying or restarting a checkpoint
Complete chapter 1 in the Single Player Campaign
Kill 25 enemies with melee attacks in Chapter 1: Why We Fight
Kill 25 enemies with a pistol in Chapter 1: Why We Fight
Find the first of 61 news pickups
Complete all other trophies for Homefront
Complete chapter 1 on the Hardest Difficulty in the Single Player Campaign
Complete chapter 2 on the Hardest Difficulty in the Single Player Campaign
Complete chapter 3 on the Hardest Difficulty in the Single Player Campaign
Complete chapter 4 on the Hardest Difficulty in the Single Player Campaign
Complete chapter 5 on the Hardest Difficulty in the Single Player Campaign
Complete chapter 6 on the Hardest Difficulty in the Single Player Campaign
Complete chapter 7 on the Hardest Difficulty in the Single Player Campaign
Complete chapter 2 in the Single Player Campaign without dying or restarting a checkpoint
Complete chapter 3 in the Single Player Campaign without dying or restarting a checkpoint
Complete chapter 4 in the Single Player Campaign without dying or restarting a checkpoint
Complete chapter 5 in the Single Player Campaign without dying or restarting a checkpoint
Complete chapter 7 in the Single Player Campaign without dying or restarting a checkpoint
Find 30 of 61 News Pickups in the Single Player Campaign
Find all 61 News Pickups in the Single Player Campaign
Complete the street section without Goliath taking any damage in Chapter 4: The Wall
Knock 10 enemies off of the scaffolding during the helicopter fly-in in Chapter 7: Golden Gate
Complete an expert challenge for any weapon in Multiplayer
Complete an expert challenge for any drone in Multiplayer
Complete an expert challenge for any vehicle in Multiplayer
Complete all challenges for weapons, drones, vehicles, and modes in Multiplayer
Reach experience level 50 in Multiplayer
Enter a public match as the Party Leader of a 4-Player Minimum Party in Multiplayer
Win a public match as the Party Leader of a Party in Multiplayer
Enter a public match in a Party with 16 players in Multiplayer
Become a 3-Star threat in a Battle Commander public match
Become a 5-Star threat in a Battle Commander public match