Example run of any% in the Demo release of the game I did a few days back. This was more a 100% run while collecting all Poke Balls and 20 berries, despite only 15 needed for unlocking the bonus stage. This means actual any% can be much faster by skipping the Poke Balls in stages 2 & 3.

Frame counted @ 30fps in avidemux to 4:51.300 from A press on beginning Stage 1.