Can the dual of a finitely-accessible category be accessible?

In Accessible Categories: The Foundations of Categorical Model Theory by Makkai and Paré, there is the example of a finitely accessible self-dual category. Apparently the example is due to Isbell. This is the category of sets and partial monomorphisms. The example appears right after Prop. 3.4.4 and right before 3.4.5.

Any locally presentable category where epimorphisms are stable under $\lambda$-codirected limits is equivalent to a complete lattice (see http://www.tac.mta.ca/tac/volumes/33/10/33-10.pdf, 3.10).