Thank you for playing, JaN!
You are correct, you need to get more power-ups especially "permanent speed upgrades" in the early levels. But you also have to use your consumables (nitros and drills). From the timestamp of your comment I could determine that you must be Guest#96. And in my database I can see, that you never used any drills (to dig through walls) or nitros (double speed for 10 turns).
But, wait a minute. There is something that you did better than anyone else so far. You are an extremely fast player. I can see this, if I go to the "global rankings" (reachable from title-screen by clicking the button "[4] global rankings"). The rankings can be sorted by different criteria. And if I sort by "Score per Hour", see who is first:
Your score might be not very high, but you "Score per Hour" is! :-)
But unfortunately it hurts my eyes that a guest is in first place here. It would be much nicer to read the name "JaN" there. So could you please register. As soon as you do, all your games you played so far as Guest#96 will be labeled with you registered username. If you leave your email and allow email-notifications, I will send you links, were you can watch the replays of your games.
Kind regards
Gerhard