Supporting learners in achieving high-level socially shared regulation of learning (SSRL) in the online collaborative learning (OCL) context presents challenges that the utilization of artificial intelligence (AI) technologies may help solve. However, the effective uses of AI to support multifaceted areas (cognition, metacognition, and motivation) and phases (forethought, performance, and reflection) of SSRL remain elusive. Furthermore, research on developing an educational AI and what pedagogical attributes and elements are required for AI to support students' SSRL effectively is limited. This study, therefore, aims to investigate students' perceptions of AI applications in enhancing SSRL and to explore the essential pedagogical elements necessary for AI to support SSRL during the OCL. To achieve these aims, the study conducted Focus Group Interviews facilitated by 9 scenarios of AI application storyboards and paper prototypes with 30 undergraduate and graduate students. The study findings show that students perceive various types of AI to support cognitive, metacognitive, and motivational areas across different SSRL phases. The study also found that students viewed AI as an active learning agent, serving in roles previously inhabited solely by human educators and students. Furthermore, the study reveals seven key pedagogical elements across TPACK components such as pedagogical, content, technological, pedagogical content, technological pedagogical, technological content, and technological pedagogical content knowledge deemed crucial by students for AI to support SSRL in OCL effectively. These findings offer implications for using and designing educationally relevant AI to support SSRL in OCL environments.