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