The sentence looks long but it’s actually a very simple sentence structure, “A wa B da” which means “A is B”.
So first we are going to look at the A part “撃っていいの”.
撃って is the te-form of the verb 撃つ meaning “to shoot” and the verb te-form followed by いい means “can do something”. So 撃っていい means “can shoot”.
And the の particle makes what comes before into a noun. It can be translated to “the one who” or “the thing which”. So 撃っていいの means “the ones who can shoot”.
Now we are going to look at the B part “撃たれる覚悟がある奴だけ”.
撃たれる is the passive form of 撃つ and it modifies 覚悟 meaning “mental preparation”, so 撃たれる覚悟 literally means “mental preparation to be shot”.
がある following a noun means “to have something”.
So 撃たれる覚悟がある literally is “to have mental preparation to be shot” which can be translated to “to be prepared to be shot” and this is the clause that modifies 奴 meaning “a person” in a casual and blunt way. So “撃たれる覚悟がある奴” means “those who are prepared to be shot”.
だけ means “only”.