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