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