It takes about 10 minutes to get to the section where you are an owl flying to catch rabbits. If you have beaten the game already, you can "Replay a Story" to replay Molly's story to get the right section.
There shouldn't be any mandatory achivements if you are trying to avoid getting any, but there are a few you might get by accident:
All Roads
Don't double back on your way to the house, just take one path
Great Owl
Once you have caught one rabbit, stop playing to avoid this achievement, or make sure that you miss a swoop deliberately so you don't get two rabbits in two swoops
So long as you stop at that section, those should be the only Achivements you need to worry about, but it's also a great game, quite short, with very easy Achivements to get 100%. It is best experienced without a guide, and I don't think there are any missable Achivements so long as you don't start a new game, but rather load your existing save, though some achievements may require you to replay a section if you didn't get it first time.