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