Not to be confused with the Crest Market, these are the in-game achievements.
For defeating 1,000 or more enemies in a single battle.
For defeating 500 or more enemies while in Awakening Mode.
For defeating 100,000 or more enemies in total.
For collecting more than 1,000,000 gold in total.
For collecting 1,000 or more weapons.
For collecting 100 or more rare materials.
For healing allies 100 or more times.
For healing three or more allies at once.
For performing 500 or more Critical Hits or Critical Rushes.
For defeating 10 or more enemies while at a disadvantage.
For dashing over 6.2 miles (10 km) on flying characters.
For dashing over 12.4 miles (20 km) while in Pair Up.
For finishing Story Mode.
For finishing Story Mode on Lunatic difficulty.
For completing all illustrations.
For collecting the maximum possible amount of one type of material.
For reaching Lv. 99 with both Rowan and Lianna.
For becoming allies with all characters.
For reaching support level A with all characters.
For receiving all blessings.
For invoking all Awakening bonuses.
For receiving over 100 amiibo presents.
For performing a Trinagle Attack.
For clearing all battles in History Mode.
For clearing all History Bode battles with an S Rank.
For clearing one History Mode battle with an S Rank.
For making all crests.
For earning all badges.
For finishing Story Mode on Hard difficulty.
For completing one illustration.
For raising the support level of two characters to A or above.
For clearing Invisible Ties in History Mode.
For clearing The Path is Yours in History Mode.
For clearing The Dark Pontifex in History Mode.
For clearing Noble Lady of Caelin in History Mode.
For clearing Together to the End in History Mode.
For clearing Grief in History Mode.
For clearing Land of Gods in History Mode.
For clearing Cold Reception in History Mode.
For clearing A Brush in the Teeth in History Mode.
For clearing Princess Minerva in History Mode.
For clearing Knorda Market in History Mode.
For clearing Scion of Legend in History Mode.
For clearing Emmeryn in History Mode.
For clearing Caravan Dancer in History Mode.
For reaching Lv. 110.
For reaching Lv. 130.
For reaching Lv. 150.
For acquiring every badge (including the DLC badges).