I cannot speak for everyone but the hard badge isn't possible for me as the game crashes before I even get close and loses all progress requiring me to start from scratch
I wish it was possible to replay only certain levels to improve the overall time, as it stands trying to do it in one hit is impossible for me especially when I get one puzzle that requires me to draw where it wants me to and not where I want pixel perfectly and resets me repeatedly turning a puzzle from seconds into a minute or more.
The shoot the missiles task is broken for me, I shoot the missile and the shot goes through the missile and blows up beyond the missile and the missile continues on to end my game
If you get the calibration screen 1st up, press ESC to get away from it. The click the rotating orb to hit the square for where you want to go up to world one. Then you Auto mode to complete each area/world by pressing A. This is all you need to do to get all badges.
The best strat to use is to go into options and enable auto-attack, then run wildly through the screens and save the guys that give you stuff. When you get the spear that you use with the right mouse button, that will be your main weapon. Duck in and out of screen and just hurl it and it will auto aim. Its then just a matter of saving up coins to buy the upgrades.
Sorry to hear that. For whatever reason, the BOTD this time around wouldn't take on a lot of browsers :(