Shovel Knight: Specter of Torment

You can do this at any time you want. I would recommend waiting until you have acquired all curios and Will and Darkness upgrades to give yourself the best chance of success. The Will Skull can help keep you alive and the Hover Plume can help prevent you from falling down any pits. Unfortunately, there is nothing in game to show you if you have destroyed all/any checkpoints in a stage you have previously completed. You need to keep track on your own.

Another option is the Cloak of Clemency (see Spec'd Out) as it will basically give you a quick retry if you accidentally die to a pit/lava/spike trap. If you have 4 Will or less, you will still instantly die. It can definitely save you from having to start the stage from scratch if you are a good ways in.