The 2:00 time is only possible by aggressively collecting bananas since bananas will add to your timer. Collecting bananas is so imporant that it's sometimes better to circle around to collect bananas in areas with large groups of them, and it's also better to go slightly slower to collect more bananas than to just blaze through. You'll want to take that shortcut path halfway through the level after the first checkpoint, and collect every bunch there even if you have to go slower to do it. Even though some of these are risky to get, it's practically mandatory for the achievement since you need to add more time on to the timer than you lose. Of course, you can absolutely miss a few bananas here and there as long as the run is clean, and you definitely shouldn't miss a platform cycle on account of a banana.