Talisman Stones allow you to equip a variety of effects. You get your first Talisman after defeating the Boss and completing the Rift Plane in Mission 3: Trial And Passage. You can equip up to three talismans at once, and each talisman can have up to three special bonus effects. Talismans are unlocked in three different ways: Mining Gravity Ore and returning the Talisman Stone for appraisal, Treasure Hunt rewards, and Event rewards. Most Talismans are earned by travelling to the mining site. Look for a yellow star icon on the map to access mining sites. These icons will not begin appearing until Chapter 2: Jirga Para Lhao, but you can also earn them in Chapter 1: Banga if you accept Side Mission 2: Fly Me To The Storm. While exploring mining sites, smash regular green gems to occasionally find basic Talismans. These are randomized, and are only appraised after you escape. Appraisal happens automatically once you return to the city hub area. Complete the indicated task to get the corresponding premium Talisman Stone:

My First Talisman
Bonus Effects: Life Extender (increases maximum health) x2
How to Unlock: Successfully complete Chapter 3: Trial And Passage.

Mining Site No. 0 Jewel
Bonus Effects: Dodge Enhancer (increases number of times you can evade/block) x2
How to Unlock: Defeat the Giant Nevi at Mining Site No. 0. Wait for a gravitational disturbance report, then return to the mining site to fight the mini-Boss.

Morning Flight
Bonus Effects: Power Extender N (Spiraling Claw lasts longer) x2, Pain Inducer N (increase damage dealt by attacks while in Normal Style; Medium Effect, cannot be stacked)
How to Unlock: Get a Gold trophy in Time Limit Battle 1.

Speedy News
Bonus Effects: Stasis Conserver N (lowers SP required to perform the Piercing Throw in Normal Style) x2
How to Unlock: Get a Gold trophy in Newspaper Delivery 2.

Cecie's Wish
Bonus Effects: Gem Detector (nearby precious gems produce a sound; cannot be stacked)
How to Unlock: Successfully complete the "If I Had Just One Wish" side mission.

Pet Lover
Bonus Effects: Breeder (dogs are attracted to Kat; cannot be stacked)
How to Unlock: Successfully complete the "Things I Like, Things I Hate" side mission.

Throwing Arm
Bonus Effects: Compressor (lowers the range for throwing objects in Stasis Field in Normal Style, but increases the damage dealt) x2
How to Unlock: Get a Gold trophy in Challenge Mission: Stasis Field Battle (Houseboat Fleet).

Golden Victory
Bonus Effects: Tonic (recover energy faster), Efficient Kick N (lowers the amount of energy required to perform a Gravity Kick), High Mileage N (while using Normal Style gravity, you do not use as much energy shifting)
How to Unlock: Successfully complete Side Mission: Dream Of The Sky.

Best Seller
Bonus Effects: Stasis Converter N (lowers the SP required to perform the Piercing Throw attack in Normal Style), Strong Arm (increases the maximum distance an object held in a Stasis Field can be thrown in Normal Style; cannot be stacked)
How to Unlock: Successfully complete Side Mission: An Author's Discreet Charm.

Azure Victory
Bonus Effects: Tonic (recover energy faster) x2
How to Unlock: Successfully complete Side Mission: Dream Of The Sky 2.