You'll have to complete the indicated task to unlock the corresponding ability:
Climb Leap - You'll have to complete Rosa's mission 'Monkey See, Monkey Do' in Sequence 7. Use this ability to make longer jumps while climbing and get hand holds that would normally be out of reach.
Disarm - For this one complete Mario's 'Evasive Maneuvers' mission in Sequence 5. Use this ability to counter incoming attacks from weapons that are normally too heavy to counter like axes and souch.
Medicines and Throwing Knives
Loot bodies to find free medicines or throwing knives.
Defeating Larger or Harder Enemies
This can only be done after learning the Disarm move not before. Now, sometimes you will run into the big 'Golden Knights' or the men who just fight better than normal soldiers. These opponents usually have unique weapons such as lances or big axes. They can also deflect attacks and counter more often, resulting in you being killed. To take them out more easily, simply disarm yourself. Put your weapon away by pressing Down. When they attack, press [X] to counter and disarm them. This usually works in one attempt. Quickly press press [X] again to kill the unarmed man.
Santa Maria della Visitazione: Giant Squid
Go to assassin's tomb. Find the large water filled room before the room where you get one of the seals required for the Armor of Altair. This room has an obstacle course. Activate the lever before going through the course and stand on the edge of the floor and look at the water. Do nothing until a large shape swims across the water. Use the lever again after the timer resets and stand on at same location. After awhile, a giant tentacle will appear.
Unlock Feather Rewards
Condottiero War Hammer - Collect 50 feathers to unlock it
Auditore Cape - Collect 100 feathers to unlock it
You'll have to accomplish the indicated achievement to get the corresponding number of Gamerscore points:
An Old Friend Returns (100 points) - Escape the hideout.
The Pain of Betrayal (30 points) - Complete DNA Sequence 1.
Vengeance (30 points) - Complete DNA Sequence 2.
Exit the Son (30 points) - Complete DNA Sequence 3.
Bloody Sunday (30 points) - Complete DNA Sequence 4.
The Conspirators (30 points) - Complete DNA Sequence 5.
An Unexpected Journey (30 points) - Complete DNA Sequence 6.
Bleeding Effect (30 points) - Complete training and reenter the Animus.
The Merchant of Venice (30 points) - Complete DNA Sequence 7.
The Impenetrable Palazzo (30 points) - Complete DNA Sequence 8.
Masquerade (30 points) - Complete DNA Sequence 9.
Bianca's Man (30 points) - Complete DNA Sequence 10.
The Prophet (30 points) - Complete DNA Sequence 11.
The Vault (30 points) - Complete DNA Sequence 14.
Podest of Monteriggioni (30 points) - Reach 80% of your stronghold's total value.
Wetland Ebony and Wetland Ivory (30 points) - In Memory of Petruccio
Doctor (20 points) - Perform an Air Assassination on a Poisoned NPC.
No-hitter (20 points) - Kill 10 enemies while remaining in conflict without being hit.
The Birth of an Assassin (20 points) - Be reborn as Ezio Auditore Da Firenze.
Arrivederci Abstergo (20 points) - Break out of Abstergo.
Welcome to the Animus 2.0 (20 points) - Enter the Animus 2.0.
Undertaker (20 points) - Discover the Assassin's Tomb inside the catacombs under Santa Maria Novella.
Vitruvian Man (20 points) - Unlock all 20 pieces of Subject 16's video.
Venetian Gladiator (20 points) - Discover the Assassin's Tomb inside Santa Maria della Visitazione.
I can see your house from here! (20 points) - Discover the Assassin's Tomb inside the Torre Grossa.
Hallowed be thy name (20 points) - Discover the Assassin's Tomb inside the Basilica di San Marco.
Prison Escape (20 points) - Discover the Assassin's Tomb inside the Rocca di Ravaldino fortress.
Choir Boy (20 points) - Discover the Assassin's Tomb inside Santa Maria del Fiore (The Duomo).
Messer Sandman (10 points) - Stun 4 guards at once by throwing sand in their face.
Street Cleaner (10 points) - Hide 5 dead bodies in a Bale of Hay.
Kleptomaniac (10 points) - Pickpocket 1000 Florins.
Lightning Strike (10 points) - Sprint for 100 meters.
Sweeper (10 points) - Sweep 5 guards at once by using a Long Weapon.
Assassin For Hire (10 points) - Complete your first assassination mission for Lorenzo Il Magnifico.
Macho Man (10 points) - Defend a woman's honor.
Steal Home (10 points) - Win a race against thieves!
Show your Colors (10 points) - Wear the Auditore cape in each city.
Handy Man (10 points) - Upgrade a building in the Stronghold.
I like the view (10 points) - Synchronize 10 View Points.
High Dive (10 points) - Perform a Leap of Faith from the Top of Florence's Giotto's Campanile.
Perfect Harmony (10 points) - Tint your clothes with those colors
Mailman (10 points) - Intercept a Borgia Courrier.
Tip of the Iceberg (10 points) - Use your Eagle Vision to scan a Glyph in the environment.
A Piece of the Puzzle (10 points) - Unlock a piece of Subject 16's video.
Collect all the Feathers. - Red Light Addict (10 points)
Spend 5000 florins on Courtesans. - Man of the People (10 points)
Toss more than 300 florins on the ground. - Victory lies in preparation (10 points)
Art Connoisseur (10 points) - Buy a Painting from Florence and Venice.
Myth Maker (5 points) - Find the 8 statuettes in Monteriggioni.
Fly Swatter (5 points) - Kick a Guard while using the Flying Machine.