The best way to achieve this is to try to beat most of the levels in under 2 minutes.
If you get to the Metropolis Zone's and have beaten every level in 2 minutes or less you'll have 32 minutes to finish Metropolis Zone 1,2,3 Sky Chase, Wing Fortress and The Death Egg Zone.
Make liberal use of the save feature, save after every level or frustrating parts that you don't want to do again if you die. Also, make sure you save before each boss fight and if you don't have any rings, save after each hit.
Even the casual gamer should be able to get this achievement with a little persistence and a lot of smart save points.
The first video is a full achievement guide.
The second video is the quickest way to get through The Death Egg zone.