Beat the game with the good ending (all bosses). The "New Game +" will be the
"clear" bat icon above your saved game slot. You can make a copy of your
existing game and then use the copy for playing New Game + in either normal or
hard mode. That way you can keep messing around in that game as well.
You do not need 100% of the souls, nor do you need to have covered 100%
of the map to finish the game, get the good ending and unlock New Game +.
To access New Game +, select the clear bat icon that appears overtop your file
(or copied file if you don't want to overwrite your original game). You get
a message saying items and souls will be transferred, with some exceptions, to
the new game. You then can decide whether you want to play in normal or hard
mode.
In New Game +, you start at the beginning of the story, but you come equipped
with all the items you had before you started New Game + and most of the souls.
However, you start with entry-level stats.
These enemies did not transfer into New Game +: Procel, Black Panther, Mudman,
Malphas, Puppet Master, Rahab, Zephyr, Bat Company, and Paranoia.
These did: Gergoth, Aguni, Death and Abaddon.
You will reacquire all the items you found and the bosses you beat before.
If you want to experience the full glory of hard mode, you can free all your
souls and sell all your items. You'll start "naked" and rich.
These are some basic differences between normal and hard mode (credit to
devilishmew, who contributed these to the message board):
* Zombies and Ghouls move faster and can poison you.
* Peeping Eyes wake up faster.
* Slimes can poison you.
* Attacks from Ghouls will knock you back and poison you.
* Draghignazzo, Barbariccia, and Malacoda will all knock you back when
attacking you.
* All Medusa Heads petrify you.
* Ukobacks get faster.
* Bone Arks fire two energy shots instead of one.
* Attacks from Tanjellies will poison AND curse you.
* Flying Armor does more damage.
* Balore gets faster.
* Puppet Master's iron maiden dolls require 4 attacks to be destroyed
instead of 2.
* Rahab drops more icicles.
* Aguni gets much faster.
* Death gets faster and his attacks become more frequent.
* Axe Armor throws axes faster.