Here is the full list of all 36 Don't Starve Together: Console Edition trophies - there are 20 bronze, 10 silver, 5 gold and 1 platinum.
You filled your trophy case to brimming.
Defeated an Ancient Guardian.
Defeated a Dragonfly.
Built a Shadow Manipulator.
Domesticated a wild beefalo.
Witnessed the miracle of Tallbird motherhood.
Defeated a Spider Queen.
Had six simultaneous pigman followers. What a party!
Hosted a public world for 40 consecutive days.
Found a hole in the ground. Wow!
Wore Snurtle Shell Armor and a Shelmet at the same time.
Had four simultaneous rock lobster followers. Snappy!
Travelled in the exact opposite of style.
Crafted a new clothing item with the help of a mysterious Innkeeper.
Defeated a Moose. Or a Goose. Or both?
Brought a friend back from the dead.
Harvested some sweet, sweet honey from an overflowing beebox.
Built a Prestihatinator.
Built a Science Machine.
Grew a pretty flower. Aw.
You felt the earth move under your feet and the sky tumblin' down.
Defeated a Bearger.
Survived 70 consecutive days.
Give resources to a new player after establishing yourself for 20 days.
Donned a fashionable character skin.
Survived 55 consecutive days.
Soothed an enraged tree.
Demonstrated your formidable sewing skills.
Survived 35 consecutive days.
Defeated a Deerclops.
Struck a deal with a large porky monarch.
Survived 20 consecutive days.
Willingly jumped down a gross hole.
Showed everyone your true feelings with an emote.
Built an Alchemy Engine.
Visited a public world.