FarCry 3 Signature Weapons unlocking Details

Signature Weapons are unlocked (but not owned by Jason until purchased) in the shops after certain criteria are met.

Signature Weapon	Condition Req'd to Unlock
Shadow	Liberate 17 Outposts.
Shredder	Collect 10 Memory Cards.
Bull	Collect 10 Relics.
Bushman	Activate all 18 Radio Towers.
Ripper	Complete six Trials of the Rakyat.
AMR	Collect 20 Relics.
Japanese Tanto	Find and collect six Letters of the Lost.

It should be noted that while signature weapons are powerful, you have no control over the attachments each one has (see individual entries); sometimes, it is better to customize a regular weapon (for example, the silenced Z93 sniper rifle) instead of using a signature weapon.

Shadow

• Unlocked by taking over 17 Enemy Camps.

  An enhanced 1911 Pistol with an extended magazine, silencer and custom paint. Enhanced for accuracy and stealth.

Shredder

• Unlocked by collecting 10 Memory Cards.

  A customized Vector .45 ACP with reflex sight, suppressor, extended magazine, and custom paint. Enhanced for accuracy and damage.

Bull

• Unlocked By Finding 10 Relics.

  A customized M133 shotgun with extended shell capacity, and custom paint. Enhanced for damage.

Bushman

• Unlocked by activating all the Radio Towers.

  A customized P416 with a optical scope, silencer, extended magazine and custom paint. Enhanced for accuracy and damage.

Ripper

• Unlocked By Completing 6 Trials of the Rakyat.

  A customized MKG with an optical scope, extended magazine and custom paint. Enhanced for accuracy, damage and low recoil.

AMR

• Unlocked by finding 20 Relics.

  A customized Z93 with extended magazine, high power scope, and custom paint. Fires an explosive, penetrating round. Enhanced for damage at long range.

Japanese Tanto

• Unlocked By Finding 6 Letters of the Lost.

  The tanto is a Japanese dagger that was carried by the samurai. Wielding one of these will increase the damage dealt in melee combat.

Source: http://www.ign.com/wikis/far-cry-3/Signature_Weapons