Here is the full list of all 56 Verdun trophies - there are 44 bronze, 10 silver, 1 gold and 1 platinum.
Acquire all other trophies.
Receive the gold medal "Most headshots" 10 times
Make 5,000 headshots
Play together with the same friend 250 times
Play together with the same friend 100 times
Receive all gold medals 10x
Receive all silver medals 10x
Play together with the same friend 50 times
Gain 250k co-op XP with a player
Receive all silver medals
Make 500 melee kills
Reach level 100
Receive the gold medal "Best advancing squad" 10 times
Reach 10,000 kills
Receive the gold medal "Best squad of match" 10 times
Receive the gold medal "Best defence squad" 10 times
Receive a total of 100 silver medals
Receive all gold medals
Make 1,000 headshots
Gain 100k co-op XP with a player
Reach level 75
Reach 5,000 kills
Gain 50k co-op XP with a player
Reach level 50
Make 100 melee kills
Gain 10k co-op XP with a player
Receive a total of 100 gold medals
Receive the gold medal "Most shots & none missed" 10 times
Receive the gold medal "10+ kills/No deaths" 10 times
Receive the gold medal "Best player" 10 times
Receive the gold medal "Most kills" 10 times
Receive the gold medal "Most headshots & only headshots" 10 times
Receive a total of 100 bronze medals
Receive the gold medal "Best Kill/Death ratio over 10 kills" 10 times
Unlock all specializations for the U.S. Doughboys
Unlock all specializations for the Belgians
Unlock all specializations for the Pioniers
Unlock all specializations for the Landser
Unlock all specializations for the Tommies
Unlock all specializations for the Poilus
Unlock all specializations for the Stoßtrupp
Unlock all specializations for the Alpenjäger
Unlock all specializations for the Canadians
Unlock all specializations for the Chasseurs
Receive the gold medal "Longest killstreak" 10 times
Reach level 25
Unlock all specializations for the Schutzen
Reach 500 kills
Kill an enemy player while you are dead
Make 10 melee kills
Make a triple kill with explosives/grenades
Make 100 headshots
Kill an enemy from over 100 meters
Join a friend
Unlock all specializations for the U.S. Marines
Kill 10 enemies as a squad NCO in 1 match