There are a total of 52 achievements. These achievements can be viewed in steam under: Community -> View all [No. of games] games -> View Stats (Under Day of Defeat: Source)
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A WOL → Play on 5 non-official Day of Defeat Source maps

Beachhead → Capture the final flag to win a round

Black Maria → Get 250 kills with the K98k's Rifle Grenade

Bolt Action → Get 500 kills with the K98k

Broomhandler → Get 150 kills with the C96

Capo → Get 500 kills with the Thompson

Carbineer → Get 150 kills with the M1 Carbine

Carpet Bomber → Get 250 kills with the Garand's Rifle Grenade

Clean Sweep → Win Dod_Colmar without the other team detonating any bombs on your objectives

Combat Engineer → Defuse 100 enemy bombs

Cookin' With Gas → Get 500 kills with the Garand

Cutthroat → Get 150 kills with the Knife

Demolition Man → Plant 100 bombs on enemy objectives

Dig For Victory! → Get 150 kills with the Shovel

Dogface → Get 1000 kills as the Rifleman player class

Don't Bring a Gun → Win a knife fight

Don't Tread on Me → Block a Flag Capture that would have won the round for the enemy team

Double Cross → Kill an enemy by throwing back one of their team's grenades or riflegrenades

Egg Layer → Get 250 kills with the US Frag Grenade

Eviction Notice → Kill a deployed sniper or machinegunner from a distance greater than 100 feet with a rocket

Hail Mary → In Dod_Jagd, plant a bomb that explodes in overtime to extend the round

Head Hunter → Get 1000 kills as the Sniper player class

HEATer → Get 1000 kills as the Rocket player class

Iron Cross → Get 5000 kills as an Axis player

Jack of All Trades → In a single life, get a kill with an MG, Sniper Rifle, Rifle, SubMG and a Grenade

Johnnie Gun → Get 500 kills with the .30 Cal

Kilroy Was Here → Score 8 machinegun kills from a single deployed position

Knuckleduster → Get 150 kills with your fists

Linoleum Ripper → Get 500 kills with the MG42

Marksman → Score 5 consecutive headshots in a single round without dying

Medal of Honor → Get 5000 kills as an Allied player

Nuts! → Block 100 Flag Captures

Old School → Get 150 kills with the Colt

On the Warpath → Score 100 Flag Captures

Point Man → Get 1000 kills as the Assault player class

Potato Masher → Get 250 kills with the Stick Grenade

Putsch → Kill a machinegunner who has killed 8 or more players from a single deployed position

Rationing → Kill 4 or more players with a single grenade, riflegrenade or bazooka shot

Rocket Powered → Get 500 kills with the Bazooka

Roscoe → Get 150 kills with the P38

Sometimes the BAR Gets You → Get 500 kills with the BAR

Squaddie → Get 1000 kills as the Support player class

Storm of the Century → Get 500 kills with the MP44

Take No Prisoners → In a single life, kill 4 or more players in the victory time after winning a round

Tank Terror → Get 500 kills with the Pschreck

The Big Burp → Get 500 kills with the MP40

The Iron Curtain → Get 1000 kills as the Machinegunner player class

The Producer → Get 500 kills with the Springfield

Trophy Collector → Score 5 or more kills in a single life using scavenged enemy weapons

War Hero → Complete all Achievements

Warlord → Win 100 rounds

Wilhelm Tell → Get 500 kills with the K98 Sniper Rifle