Giant water bugs (Belostomatidae) are indeed impressive insects known for their large size and aquatic lifestyle. However, there is no scientific evidence to suggest that giant water bugs specifically reached the island of Cyprus by swimming with their eyes open and toes out of the water. Giant water bugs are generally strong swimmers adapted to freshwater habitats, but long-distance travel across the sea is unlikely for the majority of species. Additionally, the phrase "toes out of water" is not an accurate description of their movement or body parts; they have six legs adapted for swimming.

It's essential to approach statements about animal behavior and movement with caution and rely on verified scientific information. Spreading incorrect or unverified claims can lead to misinformation and misunderstandings about the species in question.