Laser wakefield acceleration (LWFA) paves the way for the next generation of electron accelerators, for their own sake and as radiation sources. A dual-wake injection scheme is put forward here to generate an ultrabrilliant polarized attosecond electron bunch, employing a radially polarized laser as a driver. We find that the laser-modulated fields in the plasma, formed in the dual wakes excited by both transverse and longitudinal components of the laser field in the quasi-blowout regime, facilitate the attosecond injection of a transversely beamed Clover-like electron bunch. Initial spin directions of the generated attosecond electrons can be reversed collectively due to the laser-assisted spin precessions, which significantly mitigates the drastic depolarization of the sheath electrons in the strongly nonlinear plasma wake. In our three-dimensional particle-in-cell simulations, an electron bunch, with ~ 300 as duration, six-dimensional brightness of ~

and ~90% polarization can be generated using a few terawatt laser and a shock-front plasma density. Such an electron bunch could play an essential role in many applications, such as ultrafast imaging, nuclear structure studies, and the operation of coherent radiation sources.