The hard badge is pretty easy to get. The wooden projectiles are useless since they don't roll but it's good enough to get through the first 2 waves so skip the first upgrade. Then buy the iron ball and use that for about 2 levels until you can buy the set of 3 stone balls. Fire as quickly as possible so that your combos keep building between shots. Upgrade to the 3 iron balls and then the BFG.
Dragonpopking had a great comment earlier. There's no need to mess with the ball (of wood or eraser) on the last level. Add your planks onto the diagonal wooden plank already there and you can win. I tried about 20 times the pixelhunting way and then it was so easy.
It's a fun game but after going through two different birds I am stopping. Getting the last achievement of winning with all birds is not worth the grind. Like I said, it was fun the first time but it's too repetitive and there isn't a noticeable difference with the other types.
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