Complex sentence: Unwilling to wait the month required to obtain a notice of approval, she acquires a pistol illegally, and is drawn into a world of vigilantism, killing random criminals and attempting to track down the thugs who killed David.
Split into simpler sentences: Unwilling to wait the month required to obtain a notice of approval, she acquires a pistol illegally, and is drawn into a world of vigilantism, killing criminals that she encounters randomly. In the process, she attempts to track down the thugs who killed David.