Okay I have to admit that the game would do better if not for the crowbar hidden on the main map outside the gasmask room. That's just silly. Everything else made sense.
Pretty easy for a hard badge. Just pay attention to the pictures before you solve. For example, solve the rainbow by doing the blue line first, notice the red car is always in the middle, the words 'pitkin and quartz' are in the same few squares, the stars all go NE, NW, SE or SW, and so forth.
Finally got the Hard Badge!
I had lost my save game and started over from scratch. As usual, levels 14 and 15 were literally the hardest. Took me until I was level 34 and had most everything maxxed out. Pro tip for anyone who has lost their saved games: level 4 is the best level to grind early on. You get 500 or so exp and can do the entire map in about 5 minutes. It's the most cost-effective map to zoom up through the first 10 or 15 levels.
The "stunning full-motion graphics and animation" gets me every time. ;) What the hell. It was worth 15 minutes of my life to get 1 point for rating it and 5 points for reaching level 20. Now back to "Gemcraft Labyrinth."
Honestly this is the best shooter game I have ever played. It was hard, but dying gives you money so I was able to keep upgrading. "Epic boss mode" through me for a loop at level30 but each defeat just let me buy more stuff so eventually I was able to beat it. Excellent game!
Thanks Altwing! I will updating it for Kongregate in the next day or two - an achievment for completing the whole game is a really good idea!