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 75% of the Gallery.
Unlock 100% of the Gallery.
Unlock 100% of the Mystic Codes.
Unlock 100% of the Install Skills.
Cleared all Extra Stages.
Defeated two bosses in the "EX: Facsimile Fortress Nightmare" stage.
Combined two combined Install Skills.
Cleared 32 Extra Strages.
Cleared 24 Extra Stages.
Cleared 16 Extra Stages.
Cleared eight Extra Stages.
Unlock 50% of the Gallery.
Combined two Install Skills.
Raised three Servants' Bond levels to MAX.
Earned three Mystic Codes for strengthening bonds or clearing stages.
Defeat Artoria as Lancelot.
Defeated Iskandar as Darius III.
Raised a Servant's Bond level to MAX.
Used Karna's "Oh Brahma, Cover the Earth" or "Oh Brahma, Split the Earth" skills.
Cleared one Extra Stage.
Defeated Scathach as Cu Chulainn.
Cleared Stage 27 and viewed the ending.
Defeated Karna as Arjuna.
Chose to listen to Archimedes.
Cleared Stage 19 and viewed the ending.
Maxed out an Install Skill.
Cleared stage 13 or 14.
Cleared Stage 11.
Cleared Stage 18 and viewed the ending.
Cleared Stage 15 or 16.
Unlock 25% of the Gallery.
Crafted a Mystic Code.
Earned a Mystic Code for strengthening a bond or clearing a stage.
Cleared Stage 9 or 10.
Cleared Day 3.
Cleared Day 2.
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.