As irritated as Zelda is it's really not towards Sonic and more the situation. She can see that he's trying and lets out a sigh, releasing her remaining irritation with it.

"I'm Zelda, Princess of Hyrule. Link is my knight. He accompanies me everywhere." She explains, her tone much less clipped. "I'm pleased to meet you." Ignoring the part where he splashed water on her.