The fee also includes payment for the professional work needed to carry out the investigation.
Literal
Fee [in-には] investigation [object-を] do [purpose-のに] necessary professional work [toward-に対する] payment [also-も] is-included.
A densely nested noun phrase: 調査をするのに必要な専門的な仕事に対する支払い chains multiple modifiers. のに marks purpose ('in order to'), 必要な and 専門的な are stacked adjective modifiers, and に対する (toward/for) connects the work to its payment. も implies other items are already included in the fee. This noun-phrase stacking is characteristic of formal written Japanese.