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For example, $\ce{TiO2}$ is used a lot as pigments in paint, what is the range of molar absorptivity for that? Would I be able to determine this from this graph:

enter image description here

Ideally I could estimate a range for acrylic paints. I really just need a range, and it only needs to be as accurate as a few orders of magnitude.

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Well, I cannot say much from the above. Estimation of molar absorptivity experimentally would involve some measurements with different concentrations. I think single measurement may not give that information.

$TiO_{2}$ if present in paint then it is only one component ( ~10-40% or more maybe). Other components may affect the molar absorptivity too. If you want to find molar absorptivity of paint (with several components combined) you can just measure paint highly diluted in a solvent and measure UV-spectra at different known concentrations and use the Beer-lambert law.

For molar absorptivity of only $TiO_{2}$ I have different proposal.

If you have some $TiO_{2}$ then you can weigh 5 different amounts of it. Then dissolve it in acid (sulphuric acid or mixture with hydrochloric acid or you can check yourself which is better ) to make 5 solutions (should be dilute solution ). You know the concentration for these solutions.

Then, measure absorption with UV spectrometer. Finally, use the Beer-Lambert law to get the molar-absorptivity based on the absorption peak (~350 nm).

Anyway this is a weird idea. (I am not sure if absorption of acid species, say sulphate ions will affect this measurement.) And if you really try, let us know.

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