Okay, here goes. I won't bother with Kimahri's ultimate armor..

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Auron, Yuna, Tidus, Wakka, Lulu

Auto-Haste
Auto-Protect
Auto-Potion
Auto-Phoenix
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Ability: Auto-Haste

Cost: 80x Chocobo Wing
Method(s) of Retrieval:
  • Unlock Cactuar King for 99x
  • Bribe Machea (Omega Ruins - 360,000 gil) for ~60x


** See below for Cactuar King information
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Ability: Auto-Protect

Cost: 70x Light Curtain
Method(s) of Retrieval:
  • Unlock Juggernaut for 99x
  • Defeat Fafnir for 20x (40x Overkill)


** See below for Juggernaut and Fafnir information
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Ability: Auto-Potion

Cost: 4x Stamina Tablets
Method(s) of Retrieval:
  • Unlock One-Eye for 99x


** See below for One-Eye information
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Ability: Auto-Phoenix

Cost: 20x Mega Phoenix
Method(s) of Retrieval:
  • Unlock Pteryx for 99x
  • Bribe Ghost (Sunken Cave - 200,000 gil) for 40x


** See below for Pteryx information
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Rikku

Auto-Phoenix (covered)
Auto-Protect (covered)
Auto-Potion (covered)
Master Thief
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Ability: Master Thief

Cost: 30x Pendulum
Method(s) of Retrieval:
  • Win Remiem Temple race with 4 chests and no poles for 30x

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Monster: Cactuar King

HP: 100,000 (Overkill: 10,000)
AP: 8000 (Overkill: 8000)

Steal:
  • Chocobo Wing x2 (Common)
  • Designer's Wallet x1 (Rare)

Drop:
  • Blessed Gem x3 (Common) x6 (Overkill)
  • Dark Matter x1 (Rare) x2 (Overkill)


Conditions: Capture atleast one of each type of fiend in the Thunder Plains.
  • Aerouge
  • Buer
  • Melusine
  • Kusariqqu
  • Qactuar
  • Gold Element
  • Larva
  • Iron Giant


Prize for Unlocking: 99x Chocobo Wing

** You must pray at one of the Qactuar stones before Qactuar's appear in battle.
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Monster: Juggernaut

HP: 1,200,000 (Overkill: 15,000)
AP: 8000 (Overkill: 8000)

Steal:
  • Lunar Curtain x4 (Common)
  • Shining Gem x1 (Rare)

Drop:
  • Strength Sphere x1 (Common) x2 (Overkill)
  • Dark Matter x1 (Rare) x2 (Overkilll)


Conditions: Capture atleast 5 of each monster from the horned species.
  • Dual Horn (Mi'ihen Highroad)
  • Valaha (Cavern of the Stolen Fayth)
  • Grendel (Gagazet Cavern, Zanarkand Ruins)


Prize for Unlocking: Light Curtain x99
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Monster: Fafnir

HP: 1,100,000 (Overkill: 13,000)
AP: 13,000 (Overkill: 13,000)

Steal:
  • Gold Hourglass x2 (Common)
  • Stamina Spring x2 (Rare)

Drop:
  • Light Curtain x20 (Common) x40 (Overkill)
  • Dark Matter x1 (Rare) x2 (Overkill)


Conditions: Capture atleast 4 of each monster from the dragon species.
  • Vouivre (Mi'ihen Highroad)
  • Lamashtu (Mushroom Rock Road)
  • Kusariqqu (Thunder Plains)
  • Mushussu (Sanubia Desert)
  • Nidhogg (Cavern of the Stolen Fayth, Mt. Gagazet)


Prize for Unlocking: Purifying Salt x99
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Monster: One-Eye

HP: 150,000 (Overkill: 15,000)
AP: 10,000 (Overkill: 10,000)

Steal:
  • Lunar Curtain x3 (Common)
  • Blessed Gem x1 (Rare)

Drop:
  • Magic Defense Sphere x1 (Common) x2 (Overkill)
  • Dark Matter x1 (Rare) x2 (Overkill)


Conditions: Capture atleast 4 of each monster from the eyeball species.
  • Floating Eye (Mi'ihen Highroad)
  • Buer (Thunder Plains)
  • Evil Eye (Macalania Snowfield)
  • Ahriman (Mt. Gagazet, Inside Sin)
  • Floating Death (Omega Ruins)


Prize for Unlocking: Stamina Tablet x60
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Monster: Pteryx

HP: 100,000 (Overkill: 99,999)
AP: 10,000 (Overkill: 10,000)

Steal:
  • Smoke Bomb x4 (Common)
  • Candle of Life x1 (Rare)

Drop:
  • Evasion Sphere x1 (Common) x2 (Overkill)
  • Dark Matter x1 (Rare) x2 (Overkill)


Conditions: Capture atleast 4 of each monster from the bird species.
  • Condor (Besaid Island)
  • Simurgh (Djose Highroad)
  • Alcyone (Sanubia Desert)


Prize for Unlocking: Mega Phoenix x99
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*Credits for various guides at GameFAQs.

Sorry for the long post, but I thought that perhaps others may use the same armor as me, so why not help them out.