This skip has been obsoleted by a new, faster skip which can be found here: https://www.speedrun.com/wosds/guide/h7rzu (if the link is ever broken in the future, look in the "Guides" section and you should be able to find the one called "Allies Skip"

Performing this skip in your any% run will make it so you don't get all the money you would normally get from fighting Green Goblin and you don't get anyone but Black Cat to help you when in boss battles. If you do this skip so in some cases depending on your route and ability to fight bosses fast it can be faster and easier to fight Green Goblin instead of skip Night Crawler. It is faster in NG+ though.

This trick saves time in every category but some categories it may save more than others. To perform this trick once you speak to Black Cat start backtracking down to the sewers and stand right outside of the door that leads you to help nightcrawler and walk through the door and then somewhere near the edge of the platform your going to want to turn around (The tas in the video turns around and rolls that is not needed you can do the same thing but just with walking, it is faster to roll though). You will know you have done the trick correctly if you saw the door get the symbiote goo stuff on it right before you left and if you missed that you can tell by on the lower screen if not already select the "Mini Map" button and if you see Nightcrawlers head you failed the trick and you have to retry it but if you see a red "!" you did the trick correctly. Now that you have done that start heading back to the Pier and progress on with the game since Green Goblin wont be there. (Watch to the video below if you get stuck at any point in the text guide)