What makes Robin Collins' fine tuning argument stand above the rest is that he has some objective basis for the probability judgements he makes, and they are indeed impressive. Of course to do this he has to make some assumptions, which I think can actually be turned against him. What assumptions are those? Well, for starters, he assumes that any value we can plug into our equations and get a coherent description of the universe corresponds to a way the universe could have actually been. Secondly, since we don't know the probability of each of these different possible universes, he assumes they are all just as likely. There are a lot of values we can plug into the equations to get a physically coherent universe, and only a mind-bogglingly few of them would produce a life permitting universe (LPU), so with those two assumptions we get that the likelihood of a LPU is mind-bogglingly low.
Collins would then point out that since God would be both motivated to create life and have the ability to do so, it's very likely that the universe would be life permitting on Theism. On the other hand, Naturalism does nothing to raise the likelihood of a LPU; a naturalistic universe does not favour life in the same way a theistic universe would. And so theism said to be is strongly supported over naturalism by the fact out universe is life permitting.
What's unique about my objection is that, while others attack the claim that a LPU is unlikely on naturalism by defending various multiverse theories, I embrace that claim. Instead, I think there's reason to doubt that on Theism a LPU is likely. In fact I don't think it's significantly more likely on Theism than it is on Naturalism. This is because God, being omnipotent and omniscient, doesn't need a life permitting universe to create life. Notice that when Collins speaks of a life permitting universe, what he means is a universe in which life may be permitted naturally. One in which the production and sustaining of life (or embodied moral agents) may occur by the laws of nature alone, and does not require any supernatural intervention. But God is not confined by the laws of nature and, furthermore, theists commonly believe that the production and sustaining of life occurred and continues to occur supernaturally by divine intervention. Nevertheless, there is no (or, at least, very little) limitation on what God can do. If he saw fit he could have created us impervious to the cold vacuum of space, or to the extreme heat of a very young but terminally collapsing universe. God could even forgo natural law all together, and give us bodies held together by supernatural forces. And so unless the theist can meet the same requirements he puts on the atheist: come up with a non-ad hoc and independently motivated reason for why, on Theism, LPU's would be sufficiently more likely to occur, the fact that our universe is life permitting is still awkward on Theism (though maybe not as much as on Naturalism).
Theists may want to say the mere fact that God could create a LPU raises the likelihood that a LPU would exist on theism such that, while a LPU isn't expected on Theism, at least it's not unexpected—something the naturalist cannot say. I think this line of reasoning terrorizes the theistic world view, for then God's preventing the sun from rising tomorrow shouldn't be unexpected either, as it's well within his power to do so. But surely it's extremely unexpected that the sun would fail to rise tomorrow, and thus this objection forces the theist to give up too much. In fact it would dis-confirm theism, if anything. If the likelihood of something's occurring is greater given God's existence, then the fact that it does not occur is less likely given God's existence. But there are a great many things that God could make occur, and yet he does not. Every time a pink unicorn or a levitating ball isn't spontaneously created by the almighty, that's some small bit of evidence against his existence.
Notice that my objection hinges on the fact that God is powerful enough that he is not confined to the laws of nature, but could supernaturally produce and sustain life even in a universe that was not life permitting. There are other designers, though, that my objection wouldn't work against. Consider Deism, defined as the belief in a very weak creator who is not the God of monotheism, and cannot operate outside of the laws of nature. Then full force of Collins' fine tuning argument strongly supports Deism well over Theism (and over Naturalism) and, furthermore, is antithetical to both. If Deism is true, then Theism and Naturalism must both be false. But in that case, both Theism and Naturalism are more likely false than not. This would then seem to be a bitter defeat for both the atheist and the theist, but a great victory for the deist or the non-theistic design proponent (who might believe in some race of transcendent aliens who designed the universe, or something like that).
Therefore, either the fine tuning evidence and the fact that our universe is life permitting very strongly dis-confirms both Theism and Naturalism, or the assumptions made by Collins are unwarranted and it does not confirm Theism over Naturalism. And so either theists and atheists are both in a pickle, or they are both unscathed by the fine-tuning evidence.