As everyone has said, doing your core studying is best when not loaded down with classes, so you can maintain your grades while during the semester, and get more quality and time in for the DAT when you're not.
I think it also depends on which classes you're currently taking or plan to take. I wouldn't do any studying for ochem if you haven't taken both classes yet. (If it's in progress, you'll already be doing the studying for this section)
Since it sounds like you're short of time, I wouldn't attempt to spread yourself out over more than two topics of the DAT during the semesterd, I would do two things: alternate doing some PAT work and doing bio study, however we're not talking intensive bio studying, I think over the semester you should be able to slowly go through one section at a time (you might try doing the same section in KBB and Cliff's one after the other, taking notes/making flash cards (anki or paper ones); and watch videos at Khan Academy for topics that may be difficult for you to grasp (commonly photosynthesis, genetics, etc). Then reinforcing the bio will be much more efficient and not take too long, assuming you did take good notes/make good cards.
Alternatively, if you just took all your chemistry classes, you could try just doing practice problems ad nauseum, identify what you're weak in or need review. If you don't need a comprehensive chem review (It's still somewhat fresh in your head), this will save you a lot of time. Still alternating PAT practice. Either way, when the semester is over you'll have a big chunk of the DAT managed, and could probably cover the rest intensively in 1-2 months (with practice tests), taking the DAT in early-mid summer.
In any case, don't force the DAT on yourself prematurely, having to wait 3 months for a retest wouldn't be very fun, nor would getting mediocre scores, right?
