I just got the 4 and 6bi achievements. It taked a little longer 'till I realize that killing the enemies with the tukaima give a massive number of itens. I had difficult getting 4bi before that but as soon as I lined up the Tukaima with the angel it was just one go: 6.6bi at the end of the game (and the playthrough was pretty lame).
So the tip is, line up the tukaima and shot lasers like there's no tomorrow. Activate power-up mode only when the bottom counter is at 10,000. Using this method I was able to activate power-up mode up to 2 times in a single level. Reached 6 bi in the middle of final level (area 1).
Also, try to not get hit.