Every animal instinctively has the instinct for self-defense.
Literal
Self-defense instinct [topic-は] any [of-の] animal [also-も] by-birth having thing is.
どんな動物も ('every animal, any animal') uses the pattern どんな＋[noun]＋も for universal quantification. 持っているもの creates a noun phrase 'something [that is] held' — ものです provides the existential assertion. The formal/biological tone suits a nature-documentary-style statement.