목적: purpose, goal, end.
목적지: destination. 목적 + 지(place, location).
이르다: reach, or come to a place, point in time, a situation, state, etc. SYNONYM: 다다르다.
도달하다: same as 이르다, but slightly more formal.
도착하다: arrive at a place. Unlike the 이르다 and 도달하다, 도착하다 is only used with a physical place.
When talking about arriving at a final destination, 도착하다 is most commonly used.
For reaching a milestone or arriving at an interim destination, 이르다 and 도달하다 may work better.