It was hard knowing where I should go due to me being unfamiliar with the map, but I was able to collect all 20 core parts and win the game. I think I found the two secrets you mentioned as well: one was a brown door that I couldn't open, and the second one was a gold bar that can only be accessed once I collected 21 core parts.
The random effects occurring throughout the game (fastfall, extra jump, stalling in mid-air or on the ground) was a little annoying, but the robot is said to be unstable, so I'll let that slide. Spamming the dash button to dash my way through levels was my most favorite part of the game.