Generation of circularly polarized high harmonics with the same helicity to all orders is indispensable for chiral-sensitive spectroscopy with attosecond temporal resolution. Solid-state samples have added a valuable asset in controlling the polarization of emitted harmonics. However, maintaining the identical helicity of the emitted harmonics to all orders is a daunting task. In this work, we demonstrate a robust recipe for efficient generation of circularly polarized harmonics with the same helicity. For this purpose, a nontrivial tailored driving field, consisting of two co-rotating laser pulses with frequencies co and 2co, is utilized to generate harmonics from graphene. The Lissajous figure of the total driving pulse exhibits an absence of rotational symmetry, which imposes no constraint on the helicity of the emitted harmonics. Our approach to generating circularly polarized harmonics with the same helicity is robust against various per-turbations in the setup, such as variation in the subcycle phase difference or the intensity ratio of the co and 2co pulses, as rotational symmetry of the total driving pulse remains absent. Our approach is expected to be equally applicable to other two-dimensional materials, among others, transition-metal dichalcogenides and hexagonal boron nitride, as our approach is based on the absence of rotational symmetry of the driv-ing pulse. Our work paves the way for establishing compact solid-state chiral extreme ultraviolet sources, opening a realm for chiral light-matter interaction on its intrinsic timescale.