This should be the first of the 'smash 5000 blocks' achievements you will get, as the ice blocks are abundant and easy to smash.
If you play through the whole game, you'll probably not be far off 5000 (depending on how many levels you've restarted etc). If you want to grind the last few blocks out, I found level 1-11 was quite good. I sent my first bird towards the bottom half, splitting in to 3 just before it hit the first block. The second bird down the middle and the the third bird (another splitter) towards the top half.
You should be able to smash 40+ blocks on a good run and you can reload the level as soon as you've smashed your last block; no need to wait for the score to come up or the failed level screen. Have fun!