This achievement requires that you complete all 20 bonus levels in a single session and in under 45 minutes. The timer will start when you enter the portal for the first bonus level and ends when you complete the 20th bonus level.
You can play through the levels in any order but I found it best to start at the top of the lighthouse and work your way down as levels 16 and 13 were the most difficult in my opinion.
The 45 minute requirement is pretty lenient. 40 minutes is definitely possible and 35 minutes might be possible. You can die a lot and make a lot of mistakes and still get this done in 45 minutes.
I suggest playing through all of the levels several times to learn the specifics and particulars. Here is a playlist
with individual videos showing what I felt were efficient routes through each of the levels.
And here is my successful run which is likely unhelpful as it was pretty sloppy:
This was honestly my first attempt at a real run after having figured out and practiced the levels individually over a few days. It's sort of a mess as I forgot some of the puzzle specifics on a few levels and lost a lot of time while floundering to remember how to get through. I also died a bunch although I did pretty well on what I feel are the hardest levels.