After completing the 3-Star achievements for every chapter you should be very close to getting this achievement. You can grind if you want, the level I choose was Golden Egg 14 which is linked below in the video. It will show you how to get the egg and the actual level. Scarbzscope created the video and I take no credit for it. You can usually break 50-60 blocks with one bird.
You DO NOT have to wait till the game stops and gives you the restart screen. LifeGam3r confirmed the pause and restart blocks will count.
HINT!!! To speed things up a bit, zoom all the way out so you are not constantly scrolling back to the slingshot to fire your bird.
I've been trying for my 250,000 blocks smashed and I'll play Golden Egg 14 while I boost other games on my XBox. Find something else entertaining while you do it otherwise it will make you hate this game. :(
If you have any questions just message me. Playing right now while I type this.