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