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