Here is the full list of all 44 Fate/EXTELLA LINK achievements.
Acquired all other Trophies.
Cleared Stages 1 through 27 on Very Hard.
Unlock 100% of the Gallery.
Unlock 100% of the Mystic Codes.
Cleared all Extra Stages.
Unlock 100% of the Install Skills.
Cleared 32 Extra Strages.
Defeated two bosses in the "EX: Facsimile Fortress Nightmare" stage.
Defeated Iskandar as Darius III.
Cleared 24 Extra Stages.
Combined two combined Install Skills.
Unlock 75% of the Gallery.
Cleared 16 Extra Stages.
Cleared eight Extra Stages.
Defeated Karna as Arjuna.
Combined two Install Skills.
Cleared Stage 27 and viewed the ending.
Used Karna's "Oh Brahma, Cover the Earth" or "Oh Brahma, Split the Earth" skills.
Chose to listen to Archimedes.
Cleared Stage 19 and viewed the ending.
Raised three Servants' Bond levels to MAX.
Unlock 50% of the Gallery.
Defeat Artoria as Lancelot.
Cleared stage 13 or 14.
Raised a Servant's Bond level to MAX.
Cleared Stage 11.
Defeated Scathach as Cu Chulainn.
Maxed out an Install Skill.
Cleared Stage 18 and viewed the ending.
Cleared Stage 15 or 16.
Cleared one Extra Stage.
Cleared Stage 9 or 10.
Unlock 25% of the Gallery.
Earned three Mystic Codes for strengthening bonds or clearing stages.
Earned a Mystic Code for strengthening a bond or clearing a stage.
Cleared Day 3.
Cleared Day 2.
Crafted a Mystic Code.
Cleared Day 1.
Executed 8 Rush Attacks in one stage.
Used a Noble Phantasm twice in one stage.
Activated Moon Drive four times in one stage.
Gained 1000 KO's in one stage.
Viewed the event in which Charlemagne first appears.