Jessica Biel, Emile Hirsch and Isabel Lucas trudged through a blizzard Monday on the fifth day of their hike with other entertainers and activists up 19,340-foot Mt. Kilimanjaro.

“It’s pretty gnarly,” Elizabeth Gore, an executive with the United Nations Foundation, and one of the participants of the trek to raise awareness of global water issues, tells PEOPLE by satellite phone. “The visibility is only 10 feet in front of you. And it’s cold. I’ve got six layers on.”

With just a day left of climbing before hitting the summit of the Tanzanian mountain, the group reached 16,000 feet, causing many to experience headaches and stomach problems due to the high altitude.

“We’re on the hardest route at the fastest pace, but no one has turned back,” she says. “It’s pretty kick ass that all of the climbers have made it all the way. We’re all trying to help each other get to the top.”

To keep spirits high during the down time, Biel has taught the climbers a game called Mafia, in which participants draw a picture of a character on a piece of paper, then ask other players to guess the identity.

“Jess is doing awesome,” says Gore. “She continues to bring levity yet seriousness at the same time. … We’ve played every game you can imagine – travel Scrabble, word games. And there is a lot of free-style rapping going on.”

One of the biggest challenges for the group, which includes photographer Michael Muller, and Alexandra Cousteau, granddaughter of ocean explorer, Jacques Cousteau, is getting enough sleep due to the altitude. Ethiopian-born musician, Kenna, who organized the climb up Africa’s tallest peak has only slept seven or eight hours in total throughout the past five days.

To keep their energy high for the last leg of the strenuous hike, the climbers are advised to consume between 5,000 and 10,000 calories. “We’re going to be eating, eating and eating,” says Gore.