You will need to use Disjunction Elimination (Proof by cases). As P v Q is one of your premises, assume P and derive a sentence, then assume Q and derive that same sentence; you are now allowed to discharge it. The only remaining step is using Implication Elimination to reach the goal.
1. | P v Q
2. | Q → ¬ R
3. | ¬ P
4. |_ ¬ R → ¬ S
5. | |_ P
6. | | ⊥ ⊥ Intro: 5,3
7. | | ¬ R ⊥ Elim: 6
8. | |_ Q
9. | | ¬R → Elim: 2,8
10.| ¬R v Elim: 1, 5-7,8-9
11.| ¬ S → Elim: 4,10