First of all, categorize the search criteria, and group accordingly. Reasonable categories are best determined with the input of subject matter experts and users. Tabs may be used to expose different categories, however in that case only one category can be shown at a time. Whereas with the example below all categories can be revealed. (The categories below, of course, are guesses for the purpose of illustrating the controls and interaction.)
If the search filtering options are not always used, hide it initially and provide a "Search Options" toggle button to open a category:
Once the search options are opened, or if the search options are used on every search, and if not all fields are required to filter, show the list of categories with open/close toggles and examples:
Each category can then be opened to reveal associated search criteria, and a "Search" button presented:
It's not clear in the question, but if all fields are required to filter the search options, then don't use toggles instead show all categories with associated criteria grouped together—as if the final image had all the toggles open. In that case examples would be less important.