Altair's Armour is NOT required for this
As your progress through the story you will unlock 4 new Armour sets, 6 Pouch upgrades and 3 Hidden Blades from Leonardo.
Blade Upgrades (Leonardo) - Dual Blade, Poison Blade, Pistol Upgrade
Pouch Upgrades (Tailor) - There are medium (3000Florins) and large (6000Florins) variants but if you buy the large you can save buying the medium. There are 3 types all with medium and large, Medicine, Poison and Knife. (Note you need to buy the separate Knife Upgrades)
Armour Upgrades (Blacksmith)- There are 4 different armour sets each for Greaves, Vambraces, Chest Guard and Spaulders. There 4 armour sets are - Leather, Helmschmied, Metal and Missaglias.
Blade upgrades you will get for free from Leonardo as you progress through the story with Pistol being the last one to unlock near Sequence 7/8. As for the other upgrades you need to buy them from Tailors and Blacksmiths and you will need roughly 150000Florins to buy them all.