I took a guess at all the achievements.
THIS IS SPECULATION
A Cut Above: Backstab/kill a Spy who has his revolver out.
Agent Provocateur: Backstab 10 players in one life.
Burn Notice: Stay on fire for a total of 30 seconds in one life? Survive ignition 30 times?
Come in From the Cold: Backstab a Heavy who has (recently?) dominated you.
Constructus Interruptus: Backstab an enemy Engineer as he is constructing a building (whacking on it to make it build faster).
Counter Espionage: Backstab an enemy Spy disguised as one of your teammates.
Deep Undercover: Tough one... Get x kills without getting hit by anything in x amount of time?
Die Another Way: wtf is the image supposed to be? Must be something about a death in an unintended way. Kill a Spy who backstabbed a teammate less than one second ago? Dunno...
Diplomacy: Err, is that a revolver on the icon? If so: 50 revolver kills.
Dr. Nooooo: Backstab an enemy Medic with a full UberCharge.
For Your Eyes Only: Kill an enemy (Sniper?) and give them a death cam shot of you flicking a cigarette.
FYI I am a Spy: Backstab a Medic who has healed you.
High Value Target: Hmm... Maybe backstab an enemy three times in a row?
Identity Theft: Dunno how you'd "steal" an identity, other than disguising. Either it's disguise as a class you've just killed (too easy, I think), or it's a new unlock.
Insurance Fraud: The floating plusses might be related to overhealing. Backstab an enemy while being overhealed by heir Medic?
Is It Safe?: Capture 50 Control Points (possibly on your own?).
Joint Operation: Do... something three times with another Spy. 3 assists?
May I Cut In?: That's a weird icon... The plusses might mean Medics - backstab 30 Medics? Or the 30 Medic partners?
On Her Majesty's Secret Surface: Capture/start capturing a Control Point x seconds after it unlocks.
Point Breaker: Backstab 15 enemies capturing a Control Point?
Sap Auteur: Sap and destroy 1000 buildings.
Sapsucker: Backstab an Engineer whose building(s)/Sentry you've just sapped OR sap an enemy's Sentry immediately after backstabbing him (stab-n-sap).
Skullpluggery: Kill 10 Snipers with the revolver.
Slash and Burn: Backstab a Pyro who has ignited you (and survive?).
Sleeper Agent: Get a kill while you're dead (assist) OR kill an enemy who made you feign death by shooting you.
Spies Like Us: Not sure if I get the icon. Disguise as an enemy Spy and do something...
Spymaster: 1000 backstabs.
The Man from P.U.N.C.T.U.R.E.: I... have... no... idea...
The Man with the Broken Guns: Backstab/kill an Engineer and destroy all of his buildings, 3 times OR destroy 3 of his buildings.
The Melbourne Supremacy: Backstab a Sniper who has just headshot one of your teammates?
Triplecrossed: Get three backstabs in quick succession?
Wetwork: Uh... rain? Huh? Maybe an underwater backstab.
Who’s Your Daddy?: I have no idea. Might be a Spy unlock.
You Only Shiv Thrice: Get three backstabs in 10 seconds OR in quick succession, three times.