Mega Coin Squad

This is actually far easier than it sounds. While most casual playthroughs could last you anywhere from 30 to 45 minutes (really taking your time, or with multiple deaths and retries), a speed run requires almost nothing special. Just play through each level, collecting only the necessary coins in any given level, and defeating the enemies in any level where that is required (ie. the 4th level of each world). Use what diamonds you earn to upgrade your movement abilities (Shoulder Charge, Upper Punch, Ground Pound, Double Jump) first and foremost. Coin Spawner, Coin Magnet and most weapon upgrades can help, but are not required (though Invincibility is recommended if certain enemies or levels give you a hard time).

Do your best NOT to retry, as you don't need to worry about collecting the diamonds in each level. You can afford a few deaths in early levels, but not many in later levels with longer time limits, as your wasted time can easily add up in those later levels. But, after a playthrough or two, you should be familiar with what can defeat anything and how to move around. Pick a character you're most comfortable with, and rush through the game as quickly as you can using the information here, along with your personal preferences. You will receive a time (along with your collected coins) at the end of the game. If your total time was less than 30 minutes, the achievement will unlock.