wp_terms_checklist() is an admin side function as you suspect.
I don’t recommend trying to load admin side code on the front end (especially if you are not very very familiar with its inner workings) so essentially you are left with rolling your own code to create the checklist.
You should be able to use the
wp_terms_checklist() code as a model, but it may be that that code is far more complicated than you need it to be. It is hard to tell without more detail about your specific problem.