The boy was splashing about in the washtub, sending water flying.

Literal

Boy [topic-は] washtub [possessive-の] inside [at-で] splash-splash water [object-を] splashing-was.

たらい ('washtub, basin') is traditional household equipment. ジャブジャブ is a mimetic for splashing water vigorously. 水をはねかす ('to splash water') uses はねかす ('to splash, to send flying'). The whole scene is vivid childhood energy — a kid playing in a washtub on a hot day. The mimetic does the heavy sensory lifting.