This should be interesting.

End of Part I: Complete the first part of the game
End of Part II: Complete the second part of the game
End of Game: Complete Final Fantasy VII
Master Materia: Reach the maximum level of any Materia
Master of Gil: 99,999,999 Gil (definitely via X-item exploit, which I guess won't be in this. 99% sure I've done it without, from selling master materia)
Top Level: Reach level 99 with any character
Knights of the Round: Get materia Knights of the Round
Omnislash: Get Cloud’s last Limit Break
Catastrophe: Get Barret’s last Limit Break
Chaos: Get Vincent’s last Limit Break
Great Gospel: Get Aeris’s last Limit Break
Highwind: Get Cid’s last Limit Break
Final Heaven: Get Tifa’s last Limit Break
All Creation: Get Yuffie’s last Limit Break
Cosmo Memory: Get Red XIII’s last Limit Break
Slots: Get Cait Sith’s last Limit Break
Bahamut Zero: Get materia Bahamut Zero
Ultimate Weapon: Defeat the Ultimate Weapon
Diamond Weapon: Defeat the Diamond Weapon
Ruby Weapon: Defeat the Ruby Weapon
Emerald Weapon: Defeat the Emerald Weapon
Vincent: Get Vincent on your team
Yuffie: Get Yuffie on your team
Materia Overlord: Master all Materias* (the ones that can be, presumably that's what they mean)
Battle Square: Start a battle in Battle Square
Golden Feather: Get a Gold Chocobo
Won First Battle: Win your first battle
Braver: Use Cloud’s first Limit Break
Big Shot: Use Barrett’s first Limit Break
Galian Beast: Use Vincent’s first Limit Break
Healing Wind: Use Aeris’s first Limit Break
Boost Jump: Use Cid’s first Limit Break
Beat Rush: Use Tifa’s first Limit Break
Greased Lightning: Use Yuffie’s first Limit Break
Sled Fang: Use Red XIII’s first Limit Break
Dice: Use Cait Sith’s first Limit Break

Welp, that's not too difficult. Been there done all that. There should totally be an achievement for 3 sets of master materia.