Here is the full list of all 11 Tales of Monkey Island - Chapter 3: Lair of the Leviathan trophies - there are 5 bronze, 5 silver and 1 gold.
Tried every possible Face-Off feature
Introduced Murray to everyone
Defeated DeCava and the Brotherhood
Acquired La Esponja Grande
Tried every Tarot Card combination
Tried every Locket Combination
Played the bongos repeatedly
Got one one ten thousandth of the way through the alternate solution to the Cochlea puzzle
Used all the Bile Tubes in all directions
Accepted into the Brotherhood
Convinced DeCava that Guybrush is married to Morgan