Here is the full list of all 53 FateEXTELLA achievements.
Obtained all achievements.
Cleared all stages on VERY HARD difficulty.
Succeeded 100% completion rate in the gallery.
Recorded all Mystic Codes in the gallery.
Defeated a total of 5,000 Aggressors.
Completely cleared Gilgamesh's sidestory.
Cleared all Servants' sidestories.
Completely cleared Iskandar's sidestory.
Completely cleared Lü Bu's sidestory.
Completely cleared Li Shuwen's sidestory.
Completely cleared Karna's sidestory.
Completely cleared Archimedes' sidestory.
Completely cleared Cú Chulainn's sidestory.
Completely cleared Medusa's sidestory.
Completely cleared Nameless' sidestory.
Completely cleared Jeanne D'Arc's sidestory.
Raised 3 Servant's Kizuna level to 30.
Completely cleared Gawain's sidestory.
Raised a Servant's Kizuna level to 30.
Completely cleared Elizabeth Bathory's sidestory.
Cleared the Golden Poem arc.
Recorded all Install Skills in the gallery.
Cleared Artoria Pendragon's hidden side mission, then defeated her, on four different stages.
Allied with Tamamo no Mae in the Golden Poem arc.
Prevented a Sector Trap 30 times.
Cleared the Dawn arc.
Defeated Nero Claudius in the Orchid Poem arc.
Defeated Tamamo no Mae in the Dawn arc.
Revealed the true name of your Noble Phantasm 20 times.
Cleared the Orchid Poem arc.
Defeated Altera in the Orchid Poem arc.
Defeated a total of 1,000 Aggressors.
Conquered a total of 100 sectors.
Performed 50 Moon Crux/Drives.
Completely cleared Artoria Pendragon's sidestory.
Upgraded one Install Skill by +20.
Performed 200 Extella Maneuvers.
Cleared the Flame Poem arc.
Defeated Altera in the Flame Poem arc.
Prevented a Sector Trap for the first time.
Cleared Artoria Pendragon's hidden side mission, then defeated her, once.
Succeeded 25% completion rate in the gallery.
Upgraded one Install Skill by +10.
Defeated Tamamo no Mae in the Flame Poem arc.
Performed a Moon Crux/Drive for the first time.
Equipped an Install Skill for the first ime.
Equipped a new Mystic Code.
Obtained an EX rank in the results.
Cleared the 1st stage of the Flame Poem Arc.
Revealed the true name of your Noble Phantasm for the first time.
Switched with a vice general for the first time.
Performed an Extella Maneuver for the first time.