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.
Defeated two bosses in the "EX: Facsimile Fortress Nightmare" stage.
Combined two Install Skills.
Combined two combined Install Skills.
Cleared Stages 1 through 27 on Very Hard.
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.
Cleared Stage 27 and viewed the ending.
Raised a Servant's Bond level to MAX.
Chose to listen to Archimedes.
Cleared Stage 18 and viewed the ending.
Maxed out an Install Skill.
Cleared Stage 19 and viewed the ending.
Cleared stage 13 or 14.
Cleared one Extra Stage.
Cleared Stage 11.
Earned three Mystic Codes for strengthening bonds or clearing stages.
Earned a Mystic Code for strengthening a bond or clearing a stage.
Unlock 25% of the Gallery.
Cleared Stage 15 or 16.
Cleared Stage 9 or 10.
Executed 8 Rush Attacks in one stage.
Cleared Day 3.
Crafted a Mystic Code.
Cleared Day 2.
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.