You unlock this achievement for purchasing all of the customisation items available in the "Customise" menu of the game. Simply press Back, then go to Customise on the menu that comes up.
A few things to note about this achievement.
1.) You do NOT need to upgrade every item - only purchase them. When it unlocked for me, I had several "enhancements" yet to be purchased for some of my weapons and it still unlocked.
2.) Downloadable content weapons and costumes do not count. I have about three suits sitting in my customisation menu which have yet to be purchased. This achievement still unlocked.
3.) Purchasing your last item alone is not enough to unlock the achievement. Following your final item, you must back out into the main Customisation screen (It lists "Body, Main Weapon, Unique Weapon, Wig etc.") and then it will unlock.
Just to make it 100% clear, here are the items I purchased when the achievement unlocked.
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BODY
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Custom Cyborg Body
Custom Cyborg Body (Red)
Custom Cyborg Body (Blue)
Custom Cyborg Body (Yellow)
Custom Cyborg Body (Desperado Ver.)
Suit
Mariachi Uniform
Standard Cyborg Body
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MAIN WEAPON
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High-Frequency Blade
Stun Blade
Armor Breaker
High-Frequency Long Sword
High-Frequency Wooden Sword
High-Frequency Muramasa Blade
High-Frequency Machete
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UNIQUE WEAPON
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Pole-Arm "L'Étranger"
Tactical Sai "Dystopia"
Pincer Blades "Bloodlust"
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WIG
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Infinite Wig A
Infinite Wig B
Blade Mode Wig
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LIFE
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Endurance Upgrade (1)
Endurance Upgrade (2)
Endurance Upgrade (3)
Endurance Upgrade (4)
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FUEL CELLS
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Fuel Cell Upgrade (1)
Fuel Cell Upgrade (2)
Fuel Cell Upgrade (3)
Fuel Cell Upgrade (4)
Fuel Cell Upgrade (5)
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SKILL
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Aerial Parry
Defensive Offense
Sky High
Sweep Kick
Thunder Strike
Falling Lightning
Quick Draw
Lightning Strike
Stormbringer
Marches du ciel
Lumière du ciel
Cercle de l'ange
Turbulence
Down Blast
Thanks to the 360 Guide!