Which action is an attacker taking when they attempt to gain root access on the victims system?

Privilege escalation specifically describes an attacker's attempt to move from a lower-privilege account or process to a higher one (such as root on Linux or SYSTEM on Windows), granting full control over the victim's host; gaining root access is the textbook definition of this technique.

Command injection is a vulnerability class where unsanitized user input is passed to a system shell, allowing arbitrary command execution - it is a distinct attack vector and not synonymous with gaining root access.

A rootkit is a category of malware designed to conceal itself and maintain persistent privileged access after it has already been obtained, not the act of initially gaining elevated privileges.

Command and control refers to the remote communication infrastructure attackers use to manage compromised systems, not the process of acquiring elevated permissions on a host.