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