Some few achievements have been added into the game after this thread was created. I have no ideia if free DLCs should be considered DLC so I considered them base game. Also worth saying that the name of most of those achievements is the one that was used before their related content was released.
Base GameMisc. Achievements*** Spoiler - click to reveal ***
The Bunnyhopping achievement in PAYDAY 2 worth 26 pointsJump 100 times within 30 seconds. Unlocks the "No Me Gusta" mask.
The Jump! Jump! Jump! achievement in PAYDAY 2 worth 30 pointsComplete a heist without it ever going more than 4 seconds between you jumping. Unlocks the "Dawg" mask.
The We Do It Live! achievement in PAYDAY 2 worth 42 pointsComplete the Framing Frame job on the OVERKILL difficulty or above with each crew member using no skills, wearing suits, wielding Platypus 70 sniper rifles and Judge shotguns.
The Aftershock Heist
First World Bank Heist*** Spoiler - click to reveal ***
The Hidden Hostages achievement in PAYDAY 2 worth 41 pointsComplete the First World Bank job with 6 or more hostages alive behind the wall by the elevators in the main lobby.
The Original Heisters achievement in PAYDAY 2 worth 44 pointsComplete the First World Bank job on the OVERKILL difficulty or above using the PAYDAY: The Heist crew, Reinfeld Shotguns, and Bernetti 9 Pistols.
The 1337 achievement in PAYDAY 2 worth 31 pointsComplete the First World Bank job in stealth under 13 minutes and 37 seconds.
The Cloaker Fear achievement in PAYDAY 2 worth 38 pointsComplete the First World Bank job on the OVERKILL difficulty or above by securing all additional money bags while not using the loot vent bag shortcut for the additional money bags.
The CVL+ achievement in PAYDAY 2 worth 23 pointsComplete the First World Bank job on the Death Wish difficulty or above.
The OVERDRILL achievement in PAYDAY 2 worth 34 pointsIn the First World Bank job, solve the PAYDAY: The Heist secret on the Death Wish difficulty or above and enter the OVERVAULT.
The Au Ticket achievement in PAYDAY 2 worth 23 pointsIn the First World Bank job, find the Titan safe and collect the special item inside.
Slaughterhouse Heist*** Spoiler - click to reveal ***
The Not Hard Enough achievement in PAYDAY 2 worth 33 pointsComplete the Slaughterhouse job on the OVERKILL difficulty or above while Captain Winters is still present on the level.
The But How? achievement in PAYDAY 2 worth 36 pointsIn the Slaughterhouse job, get the armored truck to drop without shooting at the wires on which it is suspended.
The Making a Statement achievement in PAYDAY 2 worth 41 pointsComplete the Slaughterhouse job on the OVERKILL difficulty or above without anyone killing a single sniper.
The Pyromaniacs achievement in PAYDAY 2 worth 34 pointsIn the Slaughterhouse job, pick up two gasoline tanks within 30 seconds of entering the slaughterhouse.
The Dead Meat achievement in PAYDAY 2 worth 32 pointsComplete the Slaughterhouse job on the Death Wish difficulty or above.
The Pork Royale achievement in PAYDAY 2 worth 24 pointsIn the Slaughterhouse job, find the marked pig, secure it in the container and then complete the heist on the OVERKILL difficulty or above.
Lab Rats Job
The 3rd Annual Christimas Heist*** Spoiler - click to reveal ***
The Santa Slays Slackers achievement in PAYDAY 2 worth 33 pointsIn the Santa's Workshop job, keep all the elves alive for 30 minutes after the first assault starts on the OVERKILL difficulty or above.
The Euro Bag Simulator achievement in PAYDAY 2 worth 38 pointsComplete the Santa's Workshop job after having secured at least 100 bags in the chimney on the OVERKILL difficulty or above. Unlocks the "Rudelf" mask.
The Pumped Up and Jolly achievement in PAYDAY 2 worth 38 pointsComplete the Santa's Workshop job having all players in the crew only use shotguns. Unlocks the "Christmas Cap" mask.
The Only Santa Brings Gifts achievement in PAYDAY 2 worth 35 pointsIn the Santa's Workshop job, secure 10 bags of loot without using any player equipment or assets.
DLCsPAYDAY 2: The Point Break Heists*** Spoiler - click to reveal ***
The Clean House achievement in PAYDAY 2 worth 21 pointsIn the Beneath the Mountain job, secure all of the loot from the vaults and mountain-top in the escape helicopter. Unlocks the "Tawhiri" mask, "Flow" material and "Sun Avatar" pattern.
The Commando Crew achievement in PAYDAY 2 worth 27 pointsIn the Beneath the Mountain job, open the 4 vaults that contain loot within 10 minutes of starting the heist on the OVERKILL difficulty or above.
The Juggernauts achievement in PAYDAY 2 worth 26 pointsComplete the Beneath the Mountain job on the OVERKILL difficulty or above without any player going down.
The No Scope achievement in PAYDAY 2 worth 25 pointsKill 10 enemies in a row by shooting them in the head with the Platypus 70 Sniper Rifle while not aiming down the sights. Unlocks the "Tane" mask, "Sancti" material and "Tribal Face" pattern.
The Pinpoint Landing achievement in PAYDAY 2 worth 25 pointsIn the Birth of Sky job, parachute into the diner through a hole in the roof.
The No Blood on the Carpet achievement in PAYDAY 2 worth 18 pointsIn the Birth of Sky job, release the money without having any player take health damage on the OVERKILL difficulty or above. Unlocks the "Oro" mask, "Glade" material and "Tribal Wave" pattern.
The 1... 2... 3... JUMP! achievement in PAYDAY 2 worth 21 pointsIn the Birth of Sky job, have the entire crew jump out of the airplane within 1 minute and 23 seconds on the OVERKILL difficulty or above. Unlocks the "Maui" mask, "Wade" material and "Ornamental Crown" pattern.
The Black Tie Event achievement in PAYDAY 2 worth 30 pointsComplete the Birth of Sky job, have the entire crew use only pistols and Two Piece Suits on the OVERKILL difficulty or above.
PAYDAY 2: Armored Transport (+the ones BooHooSandyy stated)