The particular scene you need to focus on is Act III scene iii, which involves a shift in the action to another part of the island. The scene opens with a royal party, and is revealed to the audience that Sebastian and Antonio are still fixed on their plan to kill Alonso. Their plan is to commit the crime in the evening, when people are exhausted and less vigilant. When the group decides to relax and take rest, Prospero enters with some spirits an they deliver a feast which they place in front of the hungry group. However, when they begin to draw near and attempt to eat the delicious food, Ariel turns up disguised as a harpy and taunts them with the memory of their cruelty towards Miranda and Prospero in the past. The feast and Ariel then vanish suddenly.
The impact of this is notable: Alonso is suddenly filled with remorse for his wrongdoings against Prospero, but Sebastian and Antonio are unchanged and decide to fight the spirits of the island. Note Sebastian's defiance in the face of the spirits:
But one fiend at a time,
I'll fight their legions o'er!
Antonio is quick to state that he will gladly be Sebastian's "second" in this battle, and they leave together.