There are 10 Riddler Trials in Batman Arkham Knight. Completing all of them will earn you the following trophies / achievements:
The Road to Hell [Bronze/ 10G]
Pieces of the Puzzle [Bronze / 10G]
The Cat and the Bat [Bronze / 10G]
Riddler on the Rampage [Bronze / 10G]
The Burning Question [Bronze / 10G]
The Primal Riddle [Bronze / 10G]
Death by Design [Bronze / 10G]
The Riddle Factory [Bronze / 10G]
Lethal Pursuits [Bronze / 10G]
Nine Lives [Bronze / 10G]
Riddle Me That [Silver / 30G]
They are all part of the side mission “Riddler’s Revenge“. You will automatically obtain this side mission very early in the game. You don’t need to find any of the Riddler trophies to play them. You will, however, need all 243 Riddler trophies to lock up Riddler in GCPD to finish this side mission! The 243 trophies are hidden around the open world. Interrogate riddler informants to reveal their locations on your world map.
To play the 10 trials you just need to go to their starting point (they must be done in the correct order). Completing a trial will immediately unlock the next one. You will also get 2 upgrade points per trial, so it’s well worth the time. After completing all 243 riddles & doing all 10 riddler trials you can lock up the Riddler in GCPD to conclude this side mission.
You can still do this after beating the main story (there is free roam after beating the game).
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Batman: Arkham Knight Trophies and Achievements:
I AM the Batman!
Reclaim your city.
A Battle Within
Fight for your sanity.
A Heart Broken in Two
Secure the secret base.
A Leap of Faith
Complete 8 different jumps over 100 meters.
Absolution
Achieve 69 Stars in AR Challenges.
Blunt Trauma
Perform every type of predator takedown.
Brutality 101
Perform 15 different combat moves in one FreeFlow.
Choice of Weapons
Use all five Batmobile weapons successfully in one tank battle.
Cold World
Destroy the first weapons cache in Gotham City.
Cycle of Violence
Use 100 Quick Gadgets while in free flow combat.
Dark Allegiances
Apprehend Scarecrow’s senior commander.
Days of Fire
Extinguish the fires in Gotham City.
Death and Glory
Take out 20 thugs with fear takedowns.
Death by Design
Obtain a key by completing the seventh Riddler trial.
Death of Innocents
Rescue station 17 fire crew.
Dirty Tricks
Achieve 3 minutes of drifting time in the Batmobile.
Double Jeopardy
Face off with an old friend.
Fortunate Son
Achieve 46 Stars in AR Challenges.
Gates of Gotham
Destroy all of the militia watchtowers.
Gotham After Midnight
Glide for 400 meters while less than 20 meters from the ground.
Gotham Underground
Defuse all of the militia explosive ordinance in Gotham City.
Jekyll & Hyde
Stop the bank heist on Miagani Island and lock up the master mind in GCPD.
Knightfall
Initiate Knightfall Protocol.
Lethal Pursuits
Obtain a key by completing the ninth Riddler trial.
Living Hell
Interrogate the Militia APC Driver.
Master of Fear
Wayne vs Crane.
Nine Lives
Obtain a key by completing the last Riddler trial.
No Man’s Land
Restore power to the bridges of Gotham City.
Pieces of the Puzzle
Obtain a key by completing the second Riddler trial.
Point of Impact
Perform 5 perfect shots in a row with the Vulcan Gun without taking damage.
Riddle Me That
Lock up the Riddler in GCPD.
Riddler on the Rampage
Obtain a key by completing the fourth Riddler trial.
Run Through the Jungle
Fly under 3 main bridges between the islands in one continuous glide.
Savage Metal
Smash 10 militia transport vehicles off the road without using the immobilizer.
Scar of the Bat
Cure the doctor.
Seduction of the Gun
Achieve 50 critical shots on light tanks.
Sins of Youth
Achieve 23 Stars in AR Challenges.
Streets of Gotham
Destroy all of the militia checkpoints.
The Burning Question
Obtain a key by completing the fifth Riddler trial.
The Cat and the Bat
Obtain a key by completing the third Riddler trial.
The Cult
Save the sacrificial victim and lock up the executioner in GCPD.
The Frequency of Fear
Scan Gotham City to pinpoint Scarecrow’s location.
The Long Halloween
Wayne vs Crane in New Story .
The Monster Machine
Track down and apprehend the serial killer.
The Primal Riddle
Obtain a key by completing the sixth Riddler trial.
The Real Deal
Takedown 20 moving cars without using the Batmobile.
The Riddle Factory
Obtain a key by completing the eighth Riddler trial.
The Road Home
Destroy all of the militia APC’s.
The Road to Hell
Successfully complete the first Riddler trial.
Touch of Death
Apprehend the weapons dealer and lock him up in GCPD.