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