Here is the official list of Call of Duty: Black Ops 2 (BO2) achievements / trophies that can be unlocked on both Xbox 360 and PlayStation 3. There are 50 achievements available and they are mostly earned by playing the singleplayer campaign and Zombies mode.
There are also multiplayer based achievements. For example, you earn achievements / trophies for reaching level 10, activating the Prestige mode for the first time and winning five games in the League Play.
No Man Left Behind
Rescue Woods.
Gathering Storm
Investigate the jungle facility.
Shifting Sands
Gather intel on Raul Menendez from Mullah Rahmaan.
Driven by Rage
Take down Menendez and his operation.
Waterlogged
Gather information on Raul Menendez' suspected terrorist plot.
What Happens in Colossus...
Find the Karma weapon.
False Profit
Capture Manuel Noriega and bring him to justice.
Deep Cover
Capture Menendez.
Sinking Star
Interrogate Menendez.
Late for the Prom
Escort the president to the secure location in downtown LA.
Death from Above
Stop Menendez once and for all.
Old Fashioned
Complete "Pyrrhic Victory", "Old Wounds", "Time And Fate", and "Suffer With Me" in Veteran.
Futurist
Complete all future levels in veteran.
Giant Accomplishment
Complete all challenges in Black Ops II.
Mission Complete
Complete all challenges in a level.
Just Gettin' Started
Complete 1 challenge in any level.
Singapore Sling
Successfully neutralize the SDC freighter at Keppel Terminal.
Desert Storm
Successfully escort the VIPs to safety.
Defender
Successfully defend FOB Spectre from incursion.
Black Ops II Master
Complete the campaign on Hardened or Veteran difficulty.
Art of War
Successfully assassinate SDC Chairman Tian Zhao.
Blind Date
Successfully rescue HVI.
Family Reunion
There are two futures.
Hey Good Looking
Plastic surgery avoided.
Showdown
A duel between rivals.
Dirty Business
Listen and think before you shoot.
Ship Shape
Reinforcements on the way.
Dead or Alive
Jailor or executioner.
Ultimate Sacrifice
Only one can survive.
Good Karma
Crack the celerium worm.
High IQ
Collect all intel. This achievement / trophy is also available in the ghosts achievements list.
Back in Time
Use a future weapon in the past.
Man of the People
Stop the brutality inflicted by the PDF.
Gun Nut
Complete a level with customized loadout.
Ten K
Minimum score 10k in every mission.
Welcome to the Club
Reach Sergeant (Level 10) in multiplayer Public Match.
Welcome to the Penthouse
Prestige once in multiplayer Public Match.
Big Leagues
Win 5 multiplayer League Play games after being placed in a division.
Trained Up
Win 10 multiplayer games while playing in Combat Training playlists.
Party Animal
Win 10 multiplayer games while playing in Party Games playlists.
Tower of Babble
In TranZit, obey the voices.
Don't Fire Until You See
In TranZit, have all doors opened without being set on fire.
The Lights Of Their Eyes
In Green Run, pacify at least 10 zombies with 1 EMP.
Undead Man's Party Bus
In TranZit, complete all additions to the bus in 1 game.
Dance On My Grave
In Green Run, acquire your Tombstone.
Standard Equipment May Vary
In TranZit, acquire 4 different equippable items in 1 game.
You Have No Power Over Me
You Have No Power Over Me.
I Don't Think They Exist
In TranZit, kill one of the denizens of the forest while it is latched onto you.
Fuel Efficient
In TranZit, use an alternative mode of transportation.
Happy Hour
In TranZit, buy 2 different perks before turning on the power.
Platinum Trophy
PlayStation 3 gamers earn this trophy after unlocking all the trophies above. This does not apply to Xbox 360 gamers.