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