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