There are 41 Trophies that can be collected.

Bronze

Out of the Frying Pan
Complete chapter 1 of episode 1.

Adventures in Babysitting
Complete chapter 2 of episode 1.

In Your Charge
Complete chapter 3 of episode 1.

Rock and a Hard Place
Complete chapter 4 of episode 1.

It's Just One Bullet
Complete chapter 5 of episode 1.

Hey, Bud
Complete chapter 6 of episode 1.

Going Hungry
Complete chapter 1 of episode 2.

Conversation Killer
Complete chapter 2 of episode 2.

Thank You for Shopping at Save Lots!
Complete chapter 3 of episode 2.

My Dinner with Mark
Complete chapter 4 of episode 2.

Taking Charlotte
Complete chapter 6 of episode 2.

You Fight Like A Dairy Farmer
Complete chapter 7 of episode 2.

Goodbye, She Quietly Says
Complete chapter 1 of episode 3.

Bad Blood
Complete chapter 2 of episode 3.

Hit The Road
Complete chapter 3 of episode 3.

Woodbury Bound
Complete chapter 4 of episode 3.

Rumbling Down the Track
Complete chapter 5 of episode 3.

Tools for the Job
Complete chapter 7 of episode 3.

Georgia's First City
Complete chapter 1 of episode 4.

Down By The River
Complete chapter 2 of episode 4.

Support Group
Complete chapter 3 of episode 4.

Bedside Manor
Complete chapter 4 of episode 4.

For Whom The Bell Tolls
Complete chapter 6 of episode 4.

The Morning After
Complete chapter 7 of episode 4.

Into The Fire
Complete chapter 1 of episode 5.

Twice Shy
Complete chapter 2 of episode 5.

There Ain't No Way
Complete chapter 3 of episode 5.

Mercy
Complete chapter 4 of episode 5.

The Marsh House
Complete chapter 5 of episode 5.

What's In The Bag?
Complete chapter 6 of episode 5.

Silver

Two Enter, One Leaves
Complete chapter 7 of episode 1.

Too Much Salt Will Kill You
Complete chapter 5 of episode 2.

Can't Save 'em All
Complete chapter 6 of episode 3.

Georgia's Last City
Complete chapter 5 of episode 4.

Stay Close To Me
Complete chapter 7 of episode 5.

Gold

Everything's Going to be Okay
Complete Episode 1: "A New Day"

It's Not Stealing If You Need It
Complete Episode 2: "Starved For Help"

Lend Me Your Ears
Complete Episode 3: "Long Road Ahead"

Penultimate
Complete Episode 4: "Around Every Corner"

What Remains
Complete Episode 5: "No Time Left"

Platinum

The Walking Dead
Earn all trophies in: "The Walking Dead"

http://www.ps3trophies.com/forums/playstation-trophy-news/15799-walking-dead-trophy-list.html