I have no real evidence to support this, and it is all hearsay that I think might be on the right path, but I have seen it be suggested that it might be the animations themselves that drain the battery so much. For such fluid animations when compared to something like the On, the device probably has a harsher strain on the batteries longevity every time it gets booted up. Add to that the camera component and the potential possibility that not much work was done to preserve the battery life on the toy by the developers - not maliciously I wouldn't think, but maybe a small oversight - when they were originally released and you've got a pet that drains battery like there is no tomorrow.
What I can say for certain is that of the people I know with Tamas, most have original pix tamas from either wave 1 or 2, and those of us with wave 1 devices definitely have to change batteries more often even with less camera or overall use. It could be that due to all of the complaints regarding the battery life Bandai decided to silently fix the issue on the second wave, making the blue and green shells last longer overall than the pink and purple. The most I have had my pink Pix last me is a little over a week, and that was a mightily busy week for me in which I had next to no time for my virtual pets. Most of the people I know with the blue one get maybe two weeks battery out of theirs. I know no one with the green shell, so can't comment on that. I just started a Party Pix confetti color for the Christmas hatch with fresh batteries, so I'll keep track on how long those last me to see if there really is a difference or if it's just coincidence between me and my friends and I just use the darn things too much even on my busy-no-time-for-nonsense weeks.
I will also agree with tamaninjacat here on turning the brightness down all the way. It doesn't save the batteries for anything close to good battery life, but it does extend the life from a couple of days to almost a week. I have also seen it said that turning the volume off helps as well, but I enjoy the beeps of my little guys, so I haven't tried this to confirm, either.