Make sure you ALWAYS manually save when start a level and utilize all 3 slots. Autosave overwrites itself on the beginning of next level so if you don't pop the speedrun trophy, load your previous manual save. You can hold the circle to skip cutscenes, jumping doesn't increase your speed, some animations are not skippable (for example: door animation). Majority of levels are fairly easy when you learn the best path.
This was the hardest for me to do. I made it with a few seconds to spare. I think there could be a shortcut as there is a platform/elevator underneath the gear slot but I didnt know how to activate it. I always activated 2 mini elevators before running with the red sphere to break the final big wall but that was taking the longest time.