Here is the full list of all 96 Final Fantasy V (Old ver.) achievements. It takes around 60-80 hours to unlock all of the achievements on Windows.
You cleared the Cloister of the Dead.
You completed the entire Bestiary.
All four characters mastered the necromancer job.
All four characters mastered the mime job.
All four characters mastered every job.
You defeated Enuo.
You defeated Neo Shinryu.
You defeated Omega Mk.II.
All four characters mastered the oracle job.
All four characters mastered the cannoneer job.
All four characters mastered the gladiator job.
You obtained the twelve legendary weapons.
"You defeated Exdeath's servants--assassins from another dimension."
You met the dwarves.
"You defeated Neo Exdeath without anyone in your party dying."
You defeated Neo Exdeath.
You defeated Shinryu.
You defeated Omega.
You completed 60% of the Bestiary.
You raised Bartz to level 75.
You raised Bartz to level 99.
You raised Lenna to level 75.
You raised Lenna to level 99.
You raised Galuf to level 75.
You raised Galuf to level 99.
You raised Faris to level 75.
You raised Faris to level 99.
You reunited with Ghido in the third world.
"You got the four tablets for unsealing the legendary weapons."
You defeated Gilgamesh again.
You defeated Exdeath.
Krile inherited Galuf's power.
You defeated 1,000 enemies.
You obtained a submarine.
You mastered lupine attack.
You met a moogle.
You discovered Faris's true identity.
You obtained an airship.
You obtained a job from the earth crystal.
You arrived in Galuf's world.
You defeated Gilgamesh.
You completed 30% of the Bestiary.
All four characters mastered the dragoon job.
All four characters mastered the ninja job.
All four characters mastered the samurai job.
All four characters mastered the chemist job.
All four characters mastered the dancer job.
All four characters mastered the ranger job.
All four characters mastered the beastmaster job.
All four characters mastered the geomancer job.
All four characters mastered the bard job.
You raised Bartz to level 50.
You raised Lenna to level 50.
You raised Galuf to level 50.
You raised Faris to level 50.
You obtained a job from the fire crystal.
You obtained a job from the water crystal.
You met Cid.
You defeated 300 enemies.
All four characters mastered the berserker job.
All four characters mastered the mystic knight job.
All four characters mastered the time mage job.
All four characters mastered the summoner job.
All four characters mastered the red mage job.
You found out Faris is a woman.
You obtained a wind drake.
You defeated 100 enemies.
You completed 10% of the Bestiary.
You earned 10,000 gil.
You earned 50,000 gil.
You earned 200,000 gil.
You earned 500,000 gil.
All four characters mastered the knight job.
All four characters mastered the monk job.
All four characters mastered the thief job.
All four characters mastered the white mage job.
All four characters mastered the black mage job.
All four characters mastered the blue mage job.
You raised Bartz to level 25.
You raised Lenna to level 25.
You raised Galuf to level 25.
You raised Faris to level 25.
You obtained a job from the wind crystal.
You raised Faris to level 10.
You obtained the pirate ship.
You raised Bartz to level 10.
You raised Lenna to level 10.
You raised Galuf to level 10.
You played a new game.
You earned all achievements.
You pinned your hopes on Gilgamesh.
You escaped from the final battle.
You defeated the mime Gogo.
You defeated 2,000 enemies.
You mastered the piano by playing all the pianos.
You opened all the treasure chests.