Here is the full list of all 59 Verdun achievements.
Gain 250k co-op XP with a player
Receive the gold medal "Most headshots & only headshots" 10 times
Play together with the same friend 250 times
Make 5,000 headshots
Receive all silver medals 10x
Receive all gold medals 10x
Gain 100k co-op XP with a player
Receive the gold medal "Most shots & none missed" 10 times
Receive the gold medal "10+ kills/No deaths" 10 times
Receive all gold medals
Unlock all specializations for the Tirailleurs
Unlock all specializations for the ANZACs
Receive the gold medal "Best Kill/Death ratio over 10 kills" 10 times
Receive the gold medal "Longest killstreak" 10 times
Receive all silver medals
Receive the gold medal "Most kills" 10 times
Receive the gold medal "Best player" 10 times
Receive the gold medal "Most headshots" 10 times
Gain 50k co-op XP with a player
Reach personal level 100
Make 1,000 headshots
Play together with the same friend 100 times
Reach 10,000 kills
Reach personal level 75
Reach 5,000 kills
Receive a total of 100 gold medals
Receive a total of 100 silver medals
Receive a total of 100 bronze medals
Play together with the same friend 50 times
Gain 10k co-op XP with a player
Reach personal level 50
Receive the gold medal "Best advancing squad" 10 times
Receive the gold medal "Best squad of match" 10 times
Receive the gold medal "Best defence squad" 10 times
Unlock all specializations for the Highlanders
Unlock all specializations for the Schutzen
Unlock all specializations for the Marines
Unlock all specializations for the Pioniere
Unlock all specializations for the Doughboys
Unlock all specializations for the Stoßtrupp
Unlock all specializations for the Belgians
Reach personal level 25
Make 500 melee kills
Make 100 headshots
Unlock all specializations for the Canadians
Unlock all specializations for the Poilus
Unlock all specializations for the Landsers
Unlock all specializations for the Alpenjäger
Unlock all specializations for the Chasseurs
Make 100 melee kills
Reach 500 kills
Make 10 melee kills
Unlock all specializations for the Tommies
Check out the credits screen
Kill an enemy player while you are dead
Kill 10 enemies as a squad NCO in 1 match
Make a triple kill with explosives/grenades
Kill an enemy from over 100 meters
Join a friend