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.

|  P v Q         premise
|  Q → ¬ R       premise
|  ¬ P           premise
|_ ¬ R → ¬ S     premise
|  |_ P          assumption
|  |  ...
|  |  ¬ R
|  |_ Q          assumption
|  |  ¬R         → elimination
|  ...
| ¬ S

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