Thanks so much for playing, and thanks very much for posting your gameplay! It's very helpful for me to see how players pick things up and interact with the game :D I'm very impressed at how quickly you figured out that shooting downwards lets you jump higher, I wasn't expecting anyone to pick up on that over the course of a single playthrough
Spoiler alert! To reach core #3 (the only core you didn't find) you start at core #5 (which gives you the slowing towers) and head left. There's a set of platforms you have to jump across that eventually lead to a tunnel going upwards. You were very close to finding it a few times in your gameplay video. Good luck, and thanks again for playing!