This isn't a guide just some tips to help out...
You need to break all the breakable checkpoints in the game.
Basically you have to make it through every level (barring a couple which have unbreakable checkpoints) destroying all checkpoints as you go. If you die you'll have to retry from the start of the level and the checkpoints you broke will remain broken unless you swap to try another stage instead. When you return you'll have to start afresh on that stage though.
Collecting as many Will of the Wisps and Darkness from within the stages is very helpful as you will have more health.
Get the Will Skull Curio from Legion in the tower asap (this will help you to regain health during boss fight and during the levels).
Get the Cloak of Clemency from Manny asap (This cloak can literally save you if you have an unfortunate instant death or something.
Also I think it's worth noting that I missed a checkpoint in the Clockwork Tower. I completed the game with no achievement then did NOT select new game plus. Went back to Clockwork Tower and broke all the checkpoints. When I killed the Tiny Tinker bosses at the end the achievement unlocked.
So this proves you could in theory... Go through all the levels building up your characters Will/Darkness/Curios and Cloaks.
You could even use the checkpoints if you wanted to be cautious. Not only for practise but you could collect some Will and Darkness maybe a bit of money too.
Then go back and attempt each level with a maxed out character for added comfort :)