The New Version route is mostly similar to the Old Version route. This page lists only differences in the New Version run.

Sewers

Before picking up the ferns quest, head on left to pick up the Ice magic quest. Then, before doing the ice elemental quest, proceed right to loot the trident. This trident is mostly identical to the weapon bought in the Catacombs, making the sequence break unnecessary.

Gardens

To kill Arborus, use two of the Speed potions you've picked up before in order to make your trident attack speed proper. It will make you attack just as fast as the infinite attacking glitch would have.

Library

Rather than a bow, use the Firebolt spell to defeat Leviathos, using the same technique to do so. Use the money you have banked here to buy a robe and candle; fireball will be your main source of damage against bosses. Proceed to the boss room. Drop all your teleportation items and potions on the floor, specifically putting healing/regeneration potions in the center of the room, so you can pick them up after landing a hit and quickly drink them when needed. The trident should be strong enough to make (relatively) short work of him.

Catacombs

On route to the boss room, on the first screen to the right of the elevator, phase door to the ladder and kill the one skeleton wizard, activate the switch to spawn the platform, then trigger the cutscene and quickly jump onto the platform afterward, open the lock during damage invulnerability and run out again. Then proceed as usual.

Tower

Make a small detour to pick up the jumping distance ring, using a heat scroll to make the room easy.

Elven Lands

As soon as you get control of the satyr, climb up the bottom ladder and hang on it in such a way that your head is hidden behind the platform; enemies won't be able to see you, so you don't have to worry about this area yet.
Learn which mobs can be skipped and which are best picked off before they become a threat. On Easy, many mobs won't aggro you immediately, allowing you to easily pick off problematic ones. Rely mostly on the Slicering halberd and fireballs. The jump distance ring is almost mandatory here since this area is filled with otherwise pixel-perfect jumps.
After destroying the crystals, return to the satyr, jump off the ladder, then use the deathmyst spell to clear out the horde of monsters that's gathered up.