"해탈한 듯한 Irene" 해탈, a Buddhist concept, means "free oneself through understanding(해) to transcend(탈) the cares of this world". It can be taken as a synonym of 열반(nirvana, enlightenment) which is more widely known in English world. So 해탈하다 is like "reach nirvana", "attain enlightenment", or "see the (ultimate) truth/light". The ㄴ ending in 해탈한 means "the person has done something", and 듯하다 "appears to be", "like", or "as if". V-ㄴ 듯한 is thus an adjectival phrase meaning "looking like he/she has V-ed". So "해탈한 듯한 Irene" means "Irene looking like she has seen the light/truth/enlightenment", "Irene looking as if she has found her peace of mind", and so on.