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