An "act of God" is a natural occurrence that is the fault of no one. Tree limbs sometimes fall without any notice or warning — there may be nothing obvious from looking at the tree that the limb was in danger of falling. Healthy trees can get quite large and be perfectly fine for many decades. In order for the landlord to be liable for that tree limb damage to your car you have to prove the landlord was negligent in some way. Just the fact that the tree stood on his property is not enough to make him liable. For the landlord to be negligent he either had to have actual knowledge that the limb was bad and in danger of falling at any time or that he should have known through the exercise of reasonable due diligence that it was bad but he failed to exercise that due diligence. Most people don't call out tree specialist to look at their trees on a routine basis. Instead, they generally call them when there is some sign of trouble with the tree that they can see.
So was there some obvious sign that the tree was not healthy or that the limb was in danger of cracking and falling off the tree? If there was and the landlord failed to timely act to deal with the problem then you may have a good claim for negligence. The problem is that if it was pretty obvious the limb was bad then the landlord might have a good defense that you voluntarily assumed the risk that the limb would fall on the car because you saw the danger and parked there anyway.
If there answer is there was no obvious sign of trouble with the tree then the issue becomes should the landlord have known the limb was at risk to fall? What would be considered a reasonable thing for the landlord to do in his preventative maintenance of the property that would have caught the issue early enough to take action to prevent this from happening? Call out a tree inspector periodically? If so, how often — every year, every five years, 10 years? Would the inspection have even found the problem?
You are the one that must prove the negligence if you sue, so you have to present evidence to show the landlord knew or should have known of the danger and failed to remedy it.