If you miss informations or if you vote negative pls leave a comment so i can improve the solution
First of all you have to get Yuffie. She can be found near Junon in the forests around Junon (the Town with the super big gun). Just fight in the forrest until you fight a little girl with a shuriken. After the battle you talk talk with her. DONT USE THE SAVE SPOT.
instead go to her and talk to her.
This will start a dialogue. You have to chose these answers and she will then follow you.
1. Not interested
3. Wait a second!
4. thats right
5. Lets hurry on
If you make anything wrong just go back to the forrest to fight her again.
The Second part will start later in the game and can be startet as soon as you get the Tiny Bronco after Rocket Town.
Leviathan can be obtained in the Pagoda side quest after the Wutai side mission.
I wouldn't like to spoil you the whole side quest and side mission.
Have Yuffi in your team and go into the Pagoda Northwest in Wutai. Beat all enemys and you get the Summon and Yuffis Limit All Creation. This is also needed for Yuffies Limit achievement.
Like all other characters finish all other Limits and use the item. Achievement done.