The petitioner on this one is a moogle called Pilika from Bhujerba. You'll find it her in the area with one of the street stalls. She'll ask you to find and take care of her pet. You can find Rocktoise in Site 2 area in Lhusu Mines (where Ba'Gamnan was).
about 16 000 HP
Resistant to Libra
He's pretty hard as for the game phase he appears in. He's strong and has a pretty high defense attribute. He can't see too well - use it and kill two skeletons that appear in this area and when you're through with them continue to Rocktoise. The fight is pretty exhausting and you wouldn't want anyone to interrupt you. His attacks are: Stone Stomp - very strong attack against one character, Sonic Turn - aimed against those standing around the turtle, Flash - blinds all heroes in range.
Bounty: 1200 gil, Hi-potion x2, Heavy Coat
After you collect your bounty talk once again with Pilika. She'll ask you to bring her diary from the Clio's Technicks shop. Agree and go to the shop. Approach the bookshelf in the corridor for staff members only and pick the diary. You'll get to choose whether read it or not, but it doesn't matter which one you choose now. Get back to Pilika and give her the diary. Now she'll ask whether you read it or not. If you said that you did you'll get Kilimweave Shirt and if you replay that you didn't you'll get Shepherd's Bolero.