Unless you check the achievement list beforehand, it's unlikely that you'll unlock this during a normal playthrough, as you're constantly trying to avoid being eaten by the whale monster to advance in the story. After completing the game, I noticed that there are multiple chapters in the early part of the game that place you near the whale monster.
A really efficient one is the
final part of Chapter 2, Dangerous Water.
You start on the rooftop of an almost completely submerged building. Directly in front of you, you'll see 2 rectangular vents. Simply run forward and a bit to the right, to fall off an overhang and into the water - the nearby monster will immediately come after you, and chomp you up. Repeat this process until you unlock the achievement. I found that each death took approximately 17-22 seconds (that being from the time you get control of Kay, to the time you get control of her again after respawning), so getting a total of 20 can be done very quickly.
As a bonus, this checkpoint can also be used to advance 2 additional cumulative achievements:
*** Spoiler - click to reveal ***Danger Swimmer (100G) - Swam long distance while whale was around
Mermaid (90G) - Swam a very long distance
In order to add to your cumulative total for both, turn completely around at the start, and jump into the pool of water created between the 4 buildings. Swimming around in this area will prompt the monster to come after you, but it can't reach you (thanks to MrSniffss and Opticon12000 for that info); this counts towards Danger Swimmer, plus any swimming will add to your total distance for Mermaid.