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 one can be done with 1 minute to spare. The 3 pillars puzzle could be the most problematic if you angle them too steep.