It sounds obvious, but make sure you learn which side of the screen each colour button is. The visible prompts disappear after the first level, so you’ll get nowhere if they’re not etched into your memory.
If you’re gagging to max out your score, be sure to complete mission objectives. These reward you with permanent multipliers, which are handy for climbing those leaderboards.
There might not be much to buy in the store, but the (relatively pricey) extra kid effectively gives you another life to play around with. It’s useful if you’re struggling to reach later stages - just expect a bit of a coin grind first, if you don’t want to hit your real-world wallet.