The latest version of No Time To Explain (v 1.3) now has a level editor. Check out the Workshop!
Here is a quick tutorial:
1. Access the Golden Orb (from main menu or World 1)
2. Click on Create Your Own Level. You can also access other people's levels from here.
3. It has all the tools used to made original No Time To Explain levels
4. You need to have both the character and the portal in the level. Doesn't matter which character, as long as you can "beat" a level by jumping into a portal.
Uploading the level is a matter of first saving, then testing and beating it. You can upload only levels you've beaten. So if you're playing someone's level, you know the creator had to have beaten it before sharing.
Good luck!
PS we also recently released an editor for SpeedRunners - you might want to check that out, too.