Jake Gyllenhaal worked hard to embody the fearless hero Prince Dastan in Prince of Persia: The Sands of Time – getting bulked up and mastering sword fighting and the acrobatic art of parkour.

One thing he couldn’t conquer? His fear of ostriches.

“They would say, ‘Don’t make any noise around the ostriches. They’ll tear out your eyes and rip out your heart.’ So, I was naturally terrified,” Gyllenhaal, 29, said with a laugh at Sunday’s London premiere of the movie, which opens May 28 in the U.S. “They look like they’re innocent, but they’re really not.”

Gyllenhaal’s costar, Gemma Arterton, can attest to his level of fear. “He was really scared,” she told PEOPLE. “He ran away, and the look on his face – it’s not acting. It’s real.”

It sounds like Arterton, 24, who plays Princess Tamina, had a better experience with animals on the Morocco set.

“I did a horse-riding stunt, which took me two weeks to rehearse,” she says. “I had to jump onto a horse while it was galloping towards me. It was pretty scary, and I’m proud of myself for doing it, and I made sure that [I looked over my shoulder] so that everyone knew it was me and not a stunt double.”