Off the main menu you can choose either time attack or adventure. I unlocked mine in time attack, but either will work fine. Grab points. Some tips.
1) Grab multiplier bubbles whenever you can, especially in bonus levels.
2) Eat schools of fish, they are worth a substantial amount extra.
3) Bite the shark's tails, it's usually a breeze and worth an extremely large amount of points.
4) If you get to the last level, and you, like most people, have about 15 lives, get points, die, get more points, die, get more points, die, repeat, until you have over 300,000 points. I had 280,000 going into the last level and cleared it with ease using this method.
5) Eat those starfish bubbles. This will also work you towards the eat 1000 starfish bubbles achievement if you don't have that yet.
And one last thing. If you do die and run out of continues and need to play through the game again to try to get your 300,000 points, start from the beginning. Yes, it's a daunting task, 40 levels of the game, but doing it from any other point will be stretching your luck. You can look at it optimistically as working towards the "Food Bank" achievement(s) listed below. If it does take you a playthrough after you've beaten adventure and time attack, I recommend "Adventure" since the fish eaten there will count towards your food bank. Might as well be efficient.