Rope Jumping Rewards
At the very beginning of the game, Vivi can participate in a Rope Jumping game in the Alexandria town square. Depending on how many jumps you manage to complete, you'll get a progressively better item. Here are the rewards:
20 jumps: 10 gil
50 jumps: Cactrot Card
100 jumps: Genji Card
200 jumps: Alexander Card
300 jumps: Cat Paw Racket
1000 jumps: King of Skipping Title

Stellazzio Quest
Talk to the lady in the house north of the Treno Combination Shop. She will tell you about a set of thirteen Stellazzio that are spread across the world. Find them all and she will reward you everytime you return. This quest is required if you want to see the game's alternate ending.
Here are the zodiac locations:
Aries: Dali; In the windmill all the way to be back (not downstairs)
Cancer: Burmecia; behind the overturned cart
Scorpio: Quan Cave spring
Gemini: Fountain at the first screen after you enter Treno; throw coins thirteen times into the fountain.
Taurus: Treno; behind the item shop.
Virgo: Black Mage Village Inn; around the beds
Libra: Madain Sari fountain
Leo: Alexandria (after raid); Left Tower near Neptune Statue
Sagittarius: Linblum; in the left side of the 3d screen up of the
Commercial Square.
Capricorn: Dargelo Library; right hand side
Aquarius: Ipsen Heritage; right hand pillar at entrance
Pisces: Treasure chest inside Invincible.
13th Stellazzio: Return to the Quan Cave that's east of Treno after collecting and returning all 12 coins.
Ultima Weapon
To get the Ultima Weapon, go back to the glacier around were Terra was (before Kujah went gangstah on it) and search around with a Chocobo and a dead pepper.
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