In a 'Long Game' there are 3 rounds with 5 puzzle blocks in each plus the Final Cut which is 1 more puzzle block but with multipliers for anyone not in 1st position (and so irrelevant for us). Each puzzle block is worth 30,000pts so it's possible (but highly improbable) to get 150,000 points per round plus another 30,000 in the Final Cut. That's 480,000pts! Easy? No.
Quite a few of the puzzle blocks require a little bit of time to answer or work out, so you're not going to get maximum points for every one and I'm sure you'll get a few wrong along the way. What I did find a huge help was abusing the Stars system. At the end of each round, the game rewards each player with stars, if a little randomly it seems. When a player has 2 or more stars they are able to gamble on increasing their score for the next puzzle block by X1.5. To do this you must use your skill to stop the moving target on your own colour. However, if you miss and it lands on another colour, they get the multiplier. So simply play a 4 player game (if you've got 4 controllers or the big button ones) and when one of the other players has 2 or more stars, use their gamble but land the target on your colour each time. You should be able to do this about 4 - 6 times, giving you the chance to earn an extra 90,000pts.
An extra tip is try and answer correctly on all four controllers as you are going along (just press the correct button on yours first) as this will make the gamble part easier as the size of each coloured segment is based on your % of the overall score. If you only answer correctly on your controller and let the others sit on zero score, the size of your coloured segment you'll need to hit will be tiny.
You'll still need to do fairly well during the whole game but it certainly makes it a lot easier. Score over 400,000pts and when the results are announced at the end, the achievement will pop.