One of the scarier moments in their lives happened while they were swimming. The GDs were swimming in the Crimea with Nicholas one day, around 1906, when a large wave came over them. It apparently barrel rolled them and while the Tsar and the other three Grand Duchess's resurfaced little five year old Anastasia got caught under the wave. Nicholas frantically dived in after her and was able to reach far enough to grab her long hair and pull her safely to shore. Aunt Olga Alexandrovna recalled being horrified in those initial moments of panic, having "gone white with terror".
I also read that while the incident didn't keep the children from ever swimming again it did compel Nicholas to build a canvas pool for his daughters as an alternative to the sometimes rocky waters of the sea.