In comparison to all the other Achievements in this game, IMO this is by far the most challenging; others may disagree, but this one took me more than 2 hours to finally accomplish. On top of that, it was luck.
Speaking of such, unless you've played this game before or you're just highly favored by the Gods, it will take a little luck no matter your gaming skill level.
Outside of that, I found the Save feature to only be somewhat helpful. Saving after each 'block' placement is pointless. Practice as much as possible. Whether that entails starting from the beginning or just playing the final stage over and over (and over) again. Practice-practice-practice. Oh, and the other P, patience.
It's true, the only way to defeat Robotnik is with a 'combo'. In fact, more than one. If you're lucky or skilled enough to set up the 4-5 hit combo, superb, you'll get this Achievement easily. Unfortunately for me (and I can't be the only gamer out there!) I had to settle for 2-3 combos. I could never reach a 4th. The speed is just too overwhelming.
If you're like me and unable to do multiple combos, my advice is set up as many 'three stick' columns as possible. When things get edgy and time is definitely not on your side, start to connect or build as many 'four stick' columns as possible as these will explode and clear instantly. Hopefully, if you clear enough stick columns and rows you will be lucky enough to randomly connect the other 'three stick' columns you've already set up into the 'four stick' ones you need and if they've connecting from below chances are they're going to be combos.
This was my last Achievement, and perhaps yours too! Don't give up! It will eventually happen for you!