There are spoilers contained within this achievement list. If you do not want to spoil the campaign or any part of the story for yourself, go back now.
Technical Difficulties 10
Attempt to access DNA Sequence 9 for the first time.
Battle Wounds 20
Complete DNA Sequence 1.
Sanctuary! Sanctuary! 20
Find a secure place to hide and re-enter the Animus.
Rome in Ruins 20
Complete DNA Sequence 2.
Complete DNA Sequence 3.
Principessa in Another Castello 20
Complete DNA Sequence 4.
Complete DNA Sequence 5.
Forget Paris 20
Complete DNA Sequence 6.
Bloody Sunday 20
Complete DNA Sequence 7.
Vittoria Agli Assassini 20
Complete DNA Sequence 8.
Requiescat In Pace 20
Complete DNA Sequence 9.
A Knife to the Heart 50
Secure the Apple of Eden.
Perfect Recall 30
Achieve 100% Synchronization with a Sequence.
Déjà vu 20
Replay a Memory.
Undertaker 2.0 20
Discover the Shrine in the Catacombe di Roma.
Golden Boy 20
Discover the Shrine in the Terme di Traiano.
Discover the Shrine in Il Colosseo.
Discover the Shrine in the Cloaca Maxima.
One-Man Wrecking Crew 20
Discover the Shrine in Palazzo Laterano.
Discover the Shrine in the Basilica di San Pietro.
Destroy the Machine Gun.
Destroy the Naval Cannon.
Destroy the Bomber.
Destroy the Tank.
Home Improvement 20
Upgrade 5 buildings in the Antico district.
Tower Offense 20
Burn All Borgia Towers.
Show Off 20
Complete 10 Guild Challenges.
.. .- — .- .-.. .. …- . 20
Solve all of Subject 16’s Puzzles.
Earn 3 gold medals from the Animus Virtual Training Program
Recruit 3 Assassins.
Welcome to the Brotherhood 20
Train a recruit up to the Rank of Assassin.
Capture the Flag 30
Remove All Borgia Flags in Rome.
In Memoriam 20
Collect All Feathers.
Dust to Dust 20
Find 1 Artifact in the Present.
Serial Killer 20
Perform a Speed Kill Streak of 10.
Spring Cleaning 10
Kill a guard with a broom.
Your Wish is Granted 10
Throw money in a well
Fly Like an Eagle 10
Jump with the parachute off the top of Castel Sant’ Angelo.
The Gloves Come Off 10
Win the highest bet at the Fights.
Mailer Daemon 20
Access your email in 2012
Synchronization Established 10
Complete an entire Session with at least one kill (Multiplayer Only).
Needle in a Haystack 5
Kill your target while hidden in a hay bale (Multiplayer Only).
Strong Closer 20
Take the lead 10 seconds before the end of the session and go on to win (Multiplayer Only).
Fast Learner 25
Kill your target and escape your pursuer in less than 10 seconds (Multiplayer Only).
Job skills 20
During Open Conflict, kill your target and escape (Multiplayer Only).
Download Complete 40
Reach Level 50 (Multiplayer Only).
Role Model 20
Get all the Co-op bonuses in 1 session (Multiplayer Only).
Score 750 points or more on a single kill (Multiplayer Only).
Abstergo Employee of the Month 20
Get every bonus at least once (Multiplayer Only).
Ahead of the Curve 20
Perform a double or a triple escape (Multiplayer Only).