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 defeated Enuo.
You raised Galuf to level 75.
You raised Bartz to level 75.
You raised Lenna to level 75.
You defeated Neo Shinryu.
You defeated Omega Mk.II.
You raised Faris to level 75.
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.
You defeated Shinryu.
You pinned your hopes on Gilgamesh.
"You got the four tablets for unsealing the legendary weapons."
You met the dwarves.
You defeated the mime Gogo.
You obtained the twelve legendary weapons.
You mastered the piano by playing all the pianos.
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 blue mage 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 dancer job.
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.
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 completed 60% of the Bestiary.
You reunited with Ghido in the third world.
You defeated Exdeath.
You defeated Gilgamesh again.
You earned 500,000 gil.
Krile inherited Galuf's power.
You obtained a submarine.
You mastered lupine attack.
You earned 200,000 gil.
You met a moogle.
You defeated Gilgamesh.
You completed 30% of the Bestiary.
You arrived in Galuf's world.
You obtained a job from the earth crystal.
All four characters mastered the bard job.
You defeated 2,000 enemies.
You obtained an airship.
You discovered Faris's true identity.
You raised Bartz to level 25.
You raised Faris to level 25.
You raised Lenna to level 25.
You raised Galuf to level 25.
You defeated 1,000 enemies.
You obtained a job from the fire crystal.
You earned 50,000 gil.
You met Cid.
You earned 10,000 gil.
You obtained a job from the water crystal.
You completed 10% of the Bestiary.
You obtained a wind drake.
You defeated 300 enemies.
You raised Lenna to level 10.
You raised Galuf to level 10.
You raised Bartz to level 10.
You raised Faris 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.
You earned all achievements.
You escaped from the final battle.
You cleared the Cloister of the Dead.
You completed the entire Bestiary.
You opened all the treasure chests.
All four characters mastered the necromancer job.
All four characters mastered every job.
You raised Bartz to level 99.
You raised Lenna to level 99.
You raised Galuf to level 99.
You raised Faris to level 99.