Here are the Assassin's Creed 2 achievements.

Achievement    -    How to unlock

• A Piece of the Puzzle (10) - Unlock a piece of Subject 16's video.
• An Old Friend Returns (100) - Escape the hideout.
• An Unexpected Journey (30) - Complete DNA Sequence 6.
• Arrivederci Abstergo (20) - Break out of Abstergo.
• Art Connoisseur (10) - Buy a Painting from Florence and Venice.
• Assassin For Hire (10) - Complete your first assassination mission for Lorenzo Il Magnifico.
• Bianca's Man (30) - Complete DNA Sequence 10.
  
• Bleeding Effect (30) - Complete training and reenter the Animus.
• Bloody Sunday (30) - Complete DNA Sequence 4.
• Choir Boy (20) - Discover the Assassin's Tomb inside Santa Maria del Fiore (The Duomo) -.
• Doctor (20) - Perform an Air Assassination on a Poisoned NPC.
• Exit the Son (30) - Complete DNA Sequence 3.
• Fly Swatter (5) - Kick a Guard while using the Flying Machine.
• Hallowed be thy name (20) - Discover the Assassin's Tomb inside the Basilica di San Marco.
• Handy Man (10) - Upgrade a building in the Stronghold.
• High Dive (10) - Perform a Leap of Faith from the Top of Florence's Giotto's Campanile.
• I can see your house from here! (20) - Discover the Assassin's Tomb inside the Torre Grossa.
• I like the view (10) - Synchronize 10 View Points.
• In Memory of Petruccio (30) - Collect all the Feathers.
• Kleptomaniac (10) - Pickpocket 1000 Florins.
• Lightning Strike (10) - Sprint for 100 meters.
• Macho Man (10) - Defend a woman's honor.
• Mailman (10) - Intercept a Borgia Courrier.
• Man of the People (10) - Toss more than 300 florins on the ground.
• Masquerade (30) - Complete DNA Sequence 9.
• Messer Sandman (10) - Stun 4 guards at once by throwing sand in their face.
• Myth Maker (5) - Find the 8 statuettes in Monteriggioni.
• No-hitter (20) - Kill 10 enemies while remaining in conflict without being hit.
• Perfect Harmony (10) - Tint your clothes with those colors: Wetland Ebony and Wetland Ivory.
• Podesta` of Monteriggioni (30) - Reach 80% of your stronghold's total value.
• Prison Escape (20) - Discover the Assassin's Tomb inside the Rocca di Ravaldino fortress.
• Red Light Addict (10) - Spend 5000 florins on Courtesans.
• Show your Colors (10) - Wear the Auditore cape in each city.
• Steal Home (10) - Win a race against thieves!
• Street Cleaner (10) - Hide 5 dead bodies in a Bale of Hay.
• Sweeper (10) - Sweep 5 guards at once by using a Long Weapon.
• The Birth of an Assassin (20) - Be reborn as Ezio Auditore Da Firenze.
• The Conspirators (30) - Complete DNA Sequence 5.
• The Impenetrable Palazzo (30) - Complete DNA Sequence 8.
• The Merchant of Venice (30) - Complete DNA Sequence 7.
• The Pain of Betrayal (30) - Complete DNA Sequence 1.
• The Prophet (30) - Complete DNA Sequence 11.
• The Vault (30) - Complete DNA Sequence 14.
• Tip of the Iceberg (10) - Use your Eagle Vision to scan a Glyph in the environment.
• Undertaker (20) - Discover the Assassin's Tomb inside the catacombs under Santa Maria Novella.
• Venetian Gladiator (20) - Discover the Assassin's Tomb inside Santa Maria della Visitazione.
• Vengeance (30) - Complete DNA Sequence 2.
• Victory lies in preparation (10) - Get all Hidden Blades, Item Pouches and Armor upgrades for Ezio.
• Vitruvian Man (20) - Unlock all 20 pieces of Subject 16's video.
• Welcome to the Animus 2.0 (20) - Enter the Animus 2.0.