Here is the full list of all 44 Fate/EXTELLA LINK achievements.
Acquired all other Trophies.
Viewed the event in which Charlemagne first appears.
Cleared Day 1.
Cleared Day 2.
Cleared Day 3.
Cleared Stage 9 or 10.
Cleared stage 13 or 14.
Cleared Stage 15 or 16.
Cleared Stage 18 and viewed the ending.
Cleared Stage 11.
Cleared Stage 19 and viewed the ending.
Chose to listen to Archimedes.
Cleared Stage 27 and viewed the ending.
Cleared one Extra Stage.
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.
Crafted a Mystic Code.
Combined two Install Skills.
Combined two combined Install Skills.
Activated Moon Drive four times in one stage.
Used a Noble Phantasm twice in one stage.
Cleared Stages 1 through 27 on Very Hard.
Maxed out an Install Skill.
Executed 8 Rush Attacks in one stage.
Gained 1000 KO's in one stage.
Earned a Mystic Code for strengthening a bond or clearing a stage.
Earned three Mystic Codes for strengthening bonds or clearing stages.
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 25% of the Gallery.
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.