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