Hein, also known as Hyne, is a major boss in Final Fantasy III and the first in the series to have the ability to shift between its weakness.
The player should use the Scholar's Study ability to see what Hein's current weakness is. Geomancer's Terrain ability works well, but physical attackers are somewhat ineffective. One should have the Scholar use any items that deal elemental damage Hein is weak against, as they will do 1,500+ damage (for example, using the Zeus' Wrath when Hein is weak to Lightning).
In the 3D remake version, Scholars can deal more damage with items. If the player was fortunate enough to obtain a Bomb Arm as a random drop in the Molten Cave, it can inflict enough damage to wipe out Hein in a single action while Hein weak against Fire. Black Mages with powerful magic will be helpful. Monks can be useful if they are up to a reasonable level (~35-45; about the level one would have if they have been using a Monk from the start of the game). Monks can deal upwards of 1,500 damage with Retaliate. A Monk at Job Level 99 can defeat Hein in a single turn.
A strategy is to equip one or more Warriors with the Flame Mail, which can be purchased from the Village of the Ancients. Players are advised to watch out for Blizzara that Hein uses, since it can deal 500+ damage to a Warrior. Players are welcome to use Antarctic Wind and the such to target Hein's weakness, which may hit around 600+ if that element isn't his weakness.
Players can use Freezing Blade as an item to test for Hein's weakness. If the damage dealt is 600+, the party should make good use of this since Ice is now Hein's weakness, and hit Hein with Antarctic Wind or Blizzara.