This achievement isn't as tough as it first seems. The first 5-10 levels may be a little tight but after that you'll have a decent chunk of time behind you. I didn't play that brilliantly (around 35,000th in the overall time attack leaderboards) but still took 15 mins into the final level.
Stay low. The pearls give you a big boost towards your next growth checkpoint.
If you're near a growth checkpoint, play safe. Don't risk death for a risky fish.
Those speedy yellow fish that turn up occasionally are worth a lot of growth. Dash after them with the A button.
The best power-up is the red fish power-up. It automatically clears all the fish that you can eat.
Once you are big enough to eat a bigger type of fish, go for those mainly. They'll help you finish the level quicker than eating lots of small ones.