Below is a list of Trials. These are harder than the Records, and are more orientated on exploring, the affinity chart and sidequests:
Unique Monsters
Hunter-in-training - Defeat any unique monster.
Pro hunter - Defeat 10 UM.
Master hunter - Defeat 100 UM.
Landmarks
First Steps - Discover any landmark.
A corner of the world - Discover 10 landmarks.
Seasoned traveller - Discover 40 landmarks.
Globetrotter - Discover 80 landmarks.
Worldly wise - Discover 150 landmarks.
Secret Areas
Explorer - Discover a secret area.
Trailblazer - Discover 6 secret areas.
Pioneer - Discover 12 secret areas.
Affinity Chart
Your first friend - Get to know a named person.
Friend number 10 - Register 10 people on affinity chart.
Fifty fine friends - Register 50 people on affinity chart.
Friend of the world - Register 120 people on affinity chart.
Meeting People
The brave protectors - Get to know all Defence Force soldiers in colony 9.
Network of knowledge - Get to know many Nopon outsied of populated areas.
The hopeful survivors - Get to know lot of people in Colony 6.
Know so many Nopon! - Get to know the Nopon living in Frontier Village.
Wings of nobility - Get to know many High Entia with small headwings.
A village of machines - Get to know numerous Machina in the Hidden Village.
Affinity Ties
The strongest tie - Help two people form a deep affinity for one another.
Constellation - Help people form an affinity for one another 10 times.
Spider's web - Help people form an affinity for one another 50 times.
Neural network - Help people form an affinity for one another 100 times.
Roots across the world - Help almost everyone form an affinity for one
another.
Area Affinity
Colony 9 celeb - Achieve 3-star affinity rating for Colony 9.
Colony 6 celeb - Achieve 3-star affinity rating for Colony 6.
Honorary Nopon - Achieve 3-star affinity rating for Frontier Village.
Honorary High Entia - Achieve 3-star affinity rating for Alcamoth.
Honorary Machina - Achieve 3-star affinity rating for Hidden Village.
Local hero - Develop 5-star affinity with the people of any area.
World hero - Develop 5-star affinity with everyone.
Heart-to-Hearts
Heartwarming - Have Heart-to-Heart go as smoothly as possible.
Heartbreaking - Have Heart-to-Heart go as badly as possible.
Pouring out your heart - Have 20 Heart-to-Hearts.
The heart of the matter - Have 40 Heart-to-Hearts.
Ace of hearts - Have all possible Heart-to-Hearts.
Quests
Problem solved! - Complete a quest.
Helpful stranger - Complete 10 quests (excluding story quests).
Generous friend - Complete 100 quests (excluding story quests).
Charitable ally - Complete 200 quests (excluding story quests).
Selfless giver - Complete 300 quests (excluding story quests).
Shaping history - Change someone's life through your actions.
Populating Colony 6
Drawing a crowd - Increase population of Colony 6 to 50 people.
Building a community - Increase population of Colony 6 to 100 people.
Bursting at the seams - Increase population of Colony 6 to 150 people.
Rebuilding Colony 6
A fixer-upper - Start reconstruction of Colony 6.
A fix on the solution - Make good progress in reconstructing Colony 6.
Good and fixed - Finish reconstructing Colony 6. Amazing!


