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