How can I write a WP_Query that is this specific?

The tax_query attribute is what you need.

You could use it like so:

$query_args = array(
    'tax_query' => array(
        'relation' => 'AND',
        array(
            'taxonomy' => 'category',
            'field'    => 'slug',
            'terms'    => array( 'slug-of-category-a' ),
        ),
        array(
            'relation' => 'OR',
            array(
                'taxonomy' => 'category',
                'field'    => 'slug',
                'terms'    => array( 'slug-of-category-b' ),
            ),
            array(
                'taxonomy' => 'category',
                'field'    => 'slug',
                'terms'    => array( 'slug-of-category-c' ),
            ),
        ),
    ),
);
$query = new WP_Query( $query_args );

Or, taking advantage of the fact that the “IN” operator (that is used in tax_query when querying terms by default) already acts as an “OR” condition, you could also write:

$query_args = array(
    'tax_query' => array(
        'relation' => 'AND',
        array(
            'taxonomy' => 'category',
            'field'    => 'slug',
            'terms'    => array( 'slug-of-category-a' ),
        ),
        array(
            'taxonomy' => 'category',
            'field'    => 'slug',
            'terms'    => array( 'slug-of-category-b', 'slug-of-category-c' ),
        ),
    ),
);
$query = new WP_Query( $query_args );

This will get posts that are both in A and:

• B,
• C,
• both B and C.

Consult the docs I linked to for more options.