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