excellent little game; the only "problem" is that, even if one "knows" what's wrong with the argument, it's not always obvious how to actually put forth that challenge.
that was surprisingly easy for a hard badge. Booster + piercing (steadily built to the top) towers on the right, tower of sticky(+magma) on the left (one lower than the piercing tower on the right end) Just right of that an eye block. Then steadily decreasing height sticky-magma towers, so that for every tower, one extra pierce block shoots over it.