Just as you would say "I was holding my breath", you would also say "The crowd was holding their breath". This is because "I" and "the crowd" are both singular. So "breath" would be correct.
If you say "They were holding their breaths", you would then also say "Bob and Alice were holding their breaths". This is because "they" and "Bob and Alice" are both plural. So "Bob and Alice held their breaths" would be correct, even though in my opinion "breath" sounds better.
Remember: In a sentence, use breath if the subject is singular and breaths if the subject is plural.