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