As a result of the blindfolded status, tears cannot be used, and Isaac must rely heavily on the erratic movement of Guppy's Hair Ball to do damage.
Because Isaac starts with 3 Guppy items, he begins the challenge as Guppy, which grants flight (a good way of avoiding damage) and generates blue flies when dealing damage with familiars or a co-op baby.
Guppy's Hair Ball also creates blue flies when dealing damage which is a feature unique to challenges where Isaac is blindfolded, making it considerably stronger than normal.
Guppy's Hair Ball is very difficult to control. It would be wise to spend the first few attempts at the challenge by practicing with it before a real attempt at completing the challenge is made.
Items that increase movement speed can make Guppy's Hair Ball somewhat easier to use. The extra speed will allow for more precise control while also increasing the range indirectly at which the Hair Ball can safely be swung.
Buying 9 Volt from a Shop or finding the Fish Tail can allow more Blue Flies to be spawned by Guppy's Head.