In nibleheim mantion, go to the second floor, through the door on the left, you will come to a screen with three rooms, the room below has nothing in it, the room to the left has a weapon for barrit which i find useless, and the room above there will be a safe.

opening the safe:
the code can be found in various parts of the mantion.
the code is right 36, left 10, right 59, right 97.

boss:
the boss fight is against the Lost Number

hp: 7000
mp: n/a

stratogy:
try to have both choco/mog summon and areis with her limit break seal evil, to paralize the boss for a few second giving you some free hits on it. when its hp drops below the half way point it will turn into one of two forms.

physical form:
it is very resistant to physical attack so use magic.

Magic form:
it is very resistant to magic attack so use physical.

After the boss:
pick up the key in the safe, and the red materia. this materia will be the Odin summon.

once you have the key from batting the lost number boss. go to the basement which is gotten to by going through the door on the right, of the second floor in the main hallways when you first enter the mantion. once down in the basment you can open a door you preveously couldn't and you will see a sorta purple and black casket. do the action button, and the lid will pop off revealing Vincent Valintine.

Talking to Vincent:
like with getting Yuffie you will be asked a seires of questions, the first one you need to answer "talk about Sephiroth.", and the second you need to answer with "who are you?" once you are done talking to him just leave and try to go back up the way you came in. then he will join your party.