Secret Sleuth - 10g
Got the Red Star Ring located in the hidden room in SEASIDE HILL Act 1 and reached the goal.
Load up Act 1 of Seaside Hill. Very early in the level you will come to three red platforms with two jumping fish shortly beyond. You want to time your jump so that you hit one of the fish and make it to the next area. If you're having trouble making it up here like I was, try equipping one of the shields like the Aqua Shield, or Homing Attack if you have either unlocked.
Stay high up and quickly make it past the next few red platforms to reach a cannon. Continue forward, don't fall now! Soon you'll see two pillars shifting up and down. Stand on them and when they are at their lowest point, head left for a Red Ring and a 1-Up.
Just finish the level and the achievement will pop.
Update - Changed the video below. Credit to Aura313Productions of Youtube for the video.