May His Death Satisfy You Just ran through Hardcore story today so im going to post a solution on how I did it. This is a VERY simple and straightforward way of running through it without even dying once. First thing is always play on NORMAL, there is no easy mode but this is the lowest difficulty.
The character I went with was the Crusader, he is a strength attribute and is best to make a Tank. Tanking is the way to stay alive, choose the Crusader and choose the following abilites:
Primary attack - Punish (Celerity Rune)
Secondary attack - Sweep attack (trip attack rune)
Defensive - Iron Skin (Steel Skin rune)
Utility - Steed Charge (Nightmare rune)
Laws - Laws of Valor (Frozen in terror rune)
Conviction - Falling sword (Part of the Clouds rune)
Passive 1 - Fervor
Passive 2 - Fanaticism
Passive 3 - Wrathful
When you are fighting Malthael you have an open arena with health wells to your left and right. Immediately use Falling sword on him, most of the time this will stun him. Then use Iron skin and Laws of Valor, this will boost yourself up in attack speed and Iron skin will help you if he hits you.
Now basic Idea, Mash your A button (Punish) and use Sweep attack when ever you are able to. If you take some bad damage use Steed Charge to run to the wells and heal up or use a health potion (LB). Constantly use your abillites Iron skin, Laws of Valor, and Falling sword, while mashing Punish ability and Sweep. The 1 thing you really need to look for is piles of mist, those will be what can severely hurt you or even kill you, if you are in a haze of mist, get out immediatly.
While fighting Malthael I didn't have a problem at all he was easy.
For your gear I can not give you specific gear, but here is a tip I used, when you pick up a new piece of gear it compares the gear and says if it increases your damage, armor or regeneration, what I did was replace each gear if there were more green arrows then red arrows, don't focus everything on damage or your character will not be able to take hits.
Note: If you die you can save your hero, hit your home button, start button while hovering over your game, manage game, and delete your save on the right side (DO NOT DELETE EVERYWHERE ONLY FROM CONSOLE) load the game up and you will get your character back, just sent back a bit.
Any questions or concerns? Message me or comment, Good luck and have fun!