Listed in order of importance

1. Immediately after combat ends, all of your blink charges are refilled, so spam whatever you have away before they come back. Picking up Quills and opening chests also fully restores your blink charges. The duck staff is the fastest staff for NG+, it gives a 15% chance to refill your blinks after each blink.

2. Projectiles and spray spells work best for clearing enemies (Lightning bolt and frost shard are top notch). Lightning wave is also very good for killing far away shield enemies and the Silk Grove boss.

3. Let the bosses kill themselves. Stack the Treasure Mantis' poison underneath him, they will explode to do a large chunk of his health. Icebeak can hit himself with his arrows. The last boss has a rather specific way to get a very quick kill. Video example here:

3.5: You can thaw out the Glacial Collection faster by hitting them with fire spells. Recommended to use them on the right two guys so that they come out around the same time as the top left guy.

4. Doing little hops down slopes will propel you forward a little bit.

Additionally, the gilded owl is the fastest character for NG+. Picking up fireball early is good so you can trigger his movement speed increase by fireballing yourself.