Bronze

Must've Got Lost
Complete "Lost in Nightmares" on any difficulty setting.

It's Just a Bad Dream!
Complete "Lost in Nightmares" with an S rank.

Kung Fu Fighting
Inflict a set amount of damage to Wesker in "Lost in Nightmares."

Wish Upon a Star
Destroy all 18 of the Score stars found throughout "Lost in Nightmares."

Getaway
Complete "Desperate Escape" on any difficulty setting.

The Great Escape
Complete "Desperate Escape" with an S rank.

Way of the Warrior
Defeat 150 enemies singlehandedly in one playthrough of "Desperate Escape."

Shoot the Messenger
Defeat 3 Agitator Majini in one playthrough of "Desperate Escape."

Silver

Night Terrors
Complete "Lost in Nightmares" on Professional

Run the Gauntlet
Complete "Desperate Escape" on Professional.

Source: http://www.ps3trophies.org/news-383-DLC-Added--Resident-Evil-5.html