Behind Lucrecia's Waterfall
This is one of the things you should do in your game. Go to Lucrecia's Waterfall once in CD2, with Vincent in your party, and you'll see some scenes from Vincent's past! Go there again right before raiding Midgar (or in CD3), again with Vincent, and get "Chaos", the Manual to learn Vincent's Level 4 Limit Break, and "Death Penalty", Vincent's Ultimate Weapon (the more enemies Vincent has killed from when you got him, the more this weapon becomes powerful!). You'll get nothing if you didn't go there at least once before on CD2!
Lucrecia's Waterfall can be found South-East of Nibelheim. Look for an enclosed lake, you'll find it. To get there, you need either a submarine or a Green, Black or Gold Chocobo. If you wat to get there with a Chocobo, just land near it and cross the mountains. With a submarine, submerge, head North to the place with the Key of the Ancients, but head left instead of right. Follow the path and you should be able to emerge in the lake. Finally, go behind the waterfall...
First Time in CD2
"Vincent..."
"That voice? It can't be... Lucrecia...?"
"Vincent...?"
"Lucrecia!"
"Stay back!"
(Vincent remembers his past...)
"Lucrecia... you're alive..."
"I wanted to disappear... I couldn't be with anyone... I wanted to die... But the Jenova inside me wouldn't let me die... Lately, I dream a lot of Sephiroth... My dear, dear child. Ever since he was born I never got to hold him, even once... Not even once. You can't call me his mother... That... is my sin..."
(Vincent steps forward.)
"Back!! Stay back!"
(He stops.)
"Vincent... Won't you please tell me?"
"......What?"
"If Sephiroth is still alive? I heard that he died five years ago. But I see him in my dreams so often... And I know that physically, like myself, he can't die so easily. Please, Vincent, tell me......"
(Cloud comes forward to Vincent, but he waves him back.)
"Lucrecia... Sephiroth is dead..."
When you're to raid Midgar, or during CD3
(Lucrecia is not here. Vincent runs towards where she was standing and finds "Chaos" and the "Death Penalty")
"Lucrecia..."
If this part does not take place, go back outside, fight 10-20 random battles, and then come back to behind the waterfall.