Must be obtained in a single playthrough. Returning to the title screen, through quitting or death, resets the progress to zero.
Setup:
Pick the first guy as your ship. Hold to fire your primary weapon, release it to move faster, and tap to perform a diagonally forward dodge in the direction you're strafing. This allows you to pass through objects unharmed, with good timing. Occasionally you'll find a power up which you must dodge into to collect. Sometimes dodging will leave a green arrow on the screen - press again to perform a chain dodge, often destroying things in the process. If you ever become a frog (!), your dodge becomes much shorter - prepare for this.
Method:
Simply spam whenever you have a free moment between the barrage of things trying to kill you.
Do the dodge manoeuvre 25 times: Achievement unlocked!