Vincent can be recruited after a short sidequest in the Shinra Mansion, found in Nibelheim.FINDING THE COMBINATION
There is a safe on the second floor in the top left room, with clues left on how to open it on the first floor to the left as soon as you enter. Each time you interact with the note, you can read a different hint. Hint answers are below.
Alternately, if you just want the answers:
If you're doing this as soon as you reach Nibelheim after Cosmo Canyon, let enemies beat you up until everyone's limits are ready. Additionally, make sure everyone has strong magic in the form of level 2 spells, Enemy Skill, or summons that aren't Choco/Mog. Heal at the inn and save outside before opening the safe.OPENING THE SAFE
To input the combination, use Left and Right and push
to confirm a number. You cannot go over the number, so if you do, just mash
to intentionally fail. When you succeed, a boss fight with Lost Number triggers.
Lost Number has 7,000 HP and hits pretty hard, but the problem is what happens when he reaches half health. His form changes depending on the hit that dropped him below half health. If it was magical, he can deal 800 damage per hit if it uses level 2 spells. If it was physical, his main attack does 800 damage, and he unlocks Lost Blow that can do 2,500 damage. Therefore, you absolutely want to be sure he goes into the magical option. Once this happens, shown by switching from two colors to one, unload with your limits and the fight should be over or close to it.
For winning, you will get Cosmo Memory, Red XIII's limit manual, the Odin materia, and the Key to the Basement.RECRUITING VINCENT
Enter the secret basement, down the stairs, and onto the next screen. There is a locked door to the left on the second screen before reaching the library. Go through this door and interact with the coffin, then ask about Sephiroth. Interact once more to name Vincent, then try to leave the basement. Vincent will stop you shortly after reaching the next screen, then join the party and unlock the achievement.