This is another one that seems hard but it really isn’t at all. You select Time Attack Mode from the main menu. In Time Attack you will have a total time of 105 minutes from the main levels by default. If you get a total time of under 30 the Special Stages become unlocked for Time Trials with a default time of 35 minutes for all Special Stages (Just press on the control stick while in Time Attack).
Only the main stages count for this though. Here is a breakdown of the time each stage overall should take.
Palmtree Panic: 1’40”00
Collision Chaos: 2’30”00
Tidal Tempest: 3’00”00
Quartz Quadrant: 2’30”00
Wacky Workbench: 3’40”00
Stardust Speedway: 3’30”00
Metallic Madness: 6’40”00
Having around these times will put you in the range of 23 minutes so you have some room to work around to still be under 25 minutes. The achievement will pop during the score tally of whatever level level got you under 25 minutes. To play a stage, select one of the seven zones to choose from and you will be given three options on the top right corner of your screen: Exit, Next, and Go. Use and to make your selections. Use Next to cycle through the three acts of each zone and select Go to start the stage. Attempt as many runs as you want to get the best time possible.
Please refer to this topic for Time Attack videos.