Reef of Fallen World:
+1 Health - fail smashing check on getting one of the hands

Circus Minor:
+1 Quick Fingers - get cypher "Prestidigitator" from failing smashing check on the rocks
+1 Tidal Affinity - learned from Tol Maguur, solve quest "Beloved Slave"
Flex Skill (+1 to any exploration, lore or conversation skill until rest) - watch Steristi work to get an amulet with this bonus [needs "Lore: Natural" on "Trained"-Level, thx to Hety and Wizu]

Cliff's Edge:
+1 Speed - win 3 times against Aidan Sitabo
+1 Speed - kill Aidan Sitabo [CONFIRMED, thx to meheartkitty]
Ability "Clawed Gauntlets" (+4 Unarmed Damage) - buy implant from Jernaugh
Ability "Jagged Memory" (+1 Melee Damage) - buy implant from Jernaugh
Ability "Encroaching Darkness" (heal 8 Health once per day) - buy implant from Jernaugh
Ability "Blood Nanites" (Immunity to Bleeding/Burn) - buy implant from Jernaugh
Ability "Numenera Analyzer" (+5% Lore: Machinery, +5% Lore: Mystical, +5% Lore: Natural) - buy implant from Jernaugh
Ability "Artificial Eyeball" (+1 Perception) - buy implant from Jernaugh

The Fifth Eye:
+1 Intelligence and +4 Health - talk to O
+1 Intelligence - let Dhama look into your head.

Underbelly:
+1 Might - "get to work" for the "Master Foreman"
+1 Might - go fishing everyday, the third item you get is cypher "Abtrucense" with permanent +1 Might

Buried Crossroads:
+1 Intelligence - use the book "The Tome of Singing Thorns" (puzzle solution: blue, red, indigo, gold, silver)
+1 Intelligence, Might or Speed - inspect the tiny lenses [CONFIRMED, needs "Lore: Mystical" on "Trained"-Level]

The Calm:
Ability "Clear Mind" (+1 Intelligence, Might and Speed) - solve quest "Infestation"

Valley of Dead Heroes:
+1 Intelligence, Might or Speed - get cypher "Savant's Slipknot" from acid pool, it increases the highest stat by 1
+1 Intelligence - determine the nature of the darkness and bind yourself with it [CONFIRMED, thx to Hety, needs "Lore: Mystical" on "Trained"-Level]

Necropolis Tomb:
+1 Lore: Machinery - visit 50 tombs and give the cypher "Philiactery" to Silver, choose teaching reward

Miel Avest:
+1 Resistence - buy cypher "Blood of the Elements" from Lady Anshe

Ioxu's Shanty:
+1 Concentration - buy cypher "Embrace the All" from Ioxu

Chiurgeon's Slump:
+1 Lore: Machinery, Lore: Natural or Lore: Mystical - buy cypher "Essence of Knowledge" from Sheen
+3* Intelligence, Might or Speed - buy cypher "Impure Essence" from Sheen,

• 
  -1 Health - play test subject during quest "What the Winds Took" (its a malus, so use other options instead)
  
  The Vast Interior:
  +1 Intelligence - after opening the passage to trade post, help traders with their cart and get cypher "Orb of Perception"
  
  Little Nihliesh:
  +1 Tidal Affinity - talk to Aen-Tozon and Kwherezimian
  +1 Intelligence and +1 Lore: Machinery - get "Ancient Spirit Cube" from Crimper and repair it
  
  The Ascension:
  +1 Speed - use "Gauntlet of Murder" dropped by Doran
  
  The Gullet:
  +2 Intelligence - get "Candy Dispenser" from Murden, use it twice to get 2 cyphers with +1 Intelligence
  
  Heart Interior:
  +2 Intelligence - dig deep into the memories of the bloom

NOTE: You can only have 4 reflection abilities active at a time. Speak with the reflections in "The Calm" to active or deactive an ability.

Ability "Nychthemeron Defense" (Enemies receive a random negative fettle when attacking you in melee) - talk to the Nychthemeron and free it, only works at night if you broke the clock [CONFIRMED, thx to Wizu]

Ability "Seria's Peace" (+1 Intelligence, Might and Speed) - solve quests "Ashen Imitation" and "The Sorrow's Prey"

Ability "Choi's Balm" (+1 Endurance) - solve quests "Endless Horror" and "Severed Child"

Ability "Choi's Balm" [upgraded] (+1 Endurance, +2 Might, +1 Intelligence) - to upgrade the ability visit Choi's grave, visit her fathers grave, talk to Ronus Cai'sul

Ability "Inifere's Madness" (+1 Might edge, +1 Intimidation, -1 Intelligence) - solve quests "Endless Horror" and "Severed Child"

Ability "Catena Intelligence" (+1 Effort for Intelligence tasks) - take Cantena into your mind (during quest "A Hilt Without a Blade")

Ability "Erritis' Luck" (Increased critical success chance) - [UNCONFIRMED, haven't got this, i think you need to make him stronger to keep him in your mind]

Ability "Artaglio's Cunning" (companions in short range gain +5 Initiative, +15% Willpower, +10% Persuasion, +20% Damage) - take him into your mind in the Gullet (only works if he was absorbed by the maw)