This Seeking Tech guide will show you the general locations for all 27 permanently missable enemies in Final Fantasy 4.
Puppet (Bestiary Entry 61)
The Puppet is an enemy that can only be found in the Tower of Zot, which is a one-time location. It will most likely spawn on the second floor.
Sorceress (Bestiary Entry 62)
The Sorceress is also exclusively encountered in the Tower of Zot. You will most likely find it on the fourth floor of the dungeon.
Black Knight (Bestiary Entry 63)
The Black Knight is also exclusive to the Tower of Zot. It spawns most frequently on the second floor.
Centaur Knight (Bestiary Entry 64)
The Centaur Knight is another enemy that can be fought in the Tower of Zot. You will most likely encounter it on the first floor.
Gremlin (Bestiary Entry 65)
The Gremlin can only be found in the Tower of Zot. It appears most often on the second floor.
Soldieress (Bestiary Entry 66)
The Soldieress only appears in the Tower of Zot. It spawns most frequently on the third and fourth floor.
Puppeteer (Bestiary Entry 67)
The Puppeteer is another enemy that you can find in the Tower of Zot. If you missed the enemy in this location, then you may be able to find it later in the Tower of Babel, which is another one-time dungeon.
Ice Lizard (Bestiary Entry 68)
The Ice Lizard exclusively resides in the Tower of Zot. You will most likely find it on the second floor.
Cold Beast (Bestiary Entry 69)
You will also find The Cold Beast in the Tower of Zot. It appears most frequently on the first floor.
Hell Turtle (Bestiary Entry 70)
The Hell Turtle is the last of the exclusive enemies in Tower of Zot. You will most likely encounter it on the first floor of the dungeon.
Naga (Bestiary Entry 87)
The Naga can only be found in the Underworld version of Tower of Babel. You should find it in a treasure chest found in the northeast room on the fourth floor. Otherwise, it is a rare random encounter in the area. For Naga to appear, you have to get the Security Eye to summon it.
Evil Doll (Bestiary Entry 88)
The Evil Doll is an exclusive enemy in the Underworld version of Tower of Babel. You will most likely encounter it on the first or second floor.
Fiery Knight (Bestiary Entry 90)
The Fiery Knight is another enemy that can only be fought in the Underworld version of Tower of Babel. It appears most frequently on the first two floors.
Chimera (Bestiary Entry 93)
The Chimera also appears exclusively in the Underworld version of Tower of Babel. You will need to get the Security Eye to spawn the Chimera on the fourth, fifth or sixth floors.
Sorcerer (Bestiary Entry 95)
The Sorcerer can only be fought in the Overworld version of the Tower of Babel, which is another one-time dungeon. It should appear on all floors.
Ghost Knight (Bestiary Entry 96)
You should also find the Ghost Knight in the Overworld version of the Tower of Babel. This enemy should appear on all floors.
Lamia Matriarch (Bestiary Entry 97)
The Lamia Matriarch is found in the Overworld version of the Tower of Babel, after you defeat the boss and drop down below to the Underworld version of the tower. You will most likely encounter this enemy on the seventh floor.
Grudger (Bestiary Entry 99)
The Grudger is an exclusive enemy in the Overworld version of the Tower of Babel. It can spawn on any floor.
Security Eye (Bestiary Entry 101)
The Security Eye is another enemy that can only be found in the Overworld version of the Tower of Babel. You should find these when opening some of the chests in the dungeon.
Mythril Golem (Bestiary Entry 105)
The Mythril Golem can also be encountered in the Overworld version of the Tower of Babel, after you beat the boss and drop down below to the Underworld version of the tower. It appears most frequently in the room you dropped down to.
Beamer (Bestiary Entry 135)
The Beamer is an enemy that you can commonly encounter in the Giant of Babel, which is a one-time only dungeon.
Centaurion (Bestiary Entry 136)
You should also encounter the Centaurion frequently in the Giant of Babel.
Mech Soldier (Bestiary Entry 137)
Another common enemy that can only be found in the Giant of Babel is the Mech Soldier.
Searcher (Bestiary Entry 138)
The Searcher is also exclusive to the Giant of Babel. You can find this enemy in chests and random encounters.
Last Arm (Bestiary Entry 139)
The Last Arm can only be found in the Giant of Babel. You can fight it after opening the chest in the Inner Path of the Giant area.
Giant Soldier (Bestiary Entry 140)
The Giant Soldier is exclusively found in the Giant of Babel. You should be able to encounter one while exploring one of the upper floors.
Mech Dragon (Bestiary Entry 141)
The Mech Dragon is the rarest encounter in the Giant of Babel. You can only find it in the Stairwell of the Giant area.