Can I use taskkill to kill a process running under a certain user?

taskkill /F /T /IM foo.exe /FI "USERNAME eq target_user"

should do it. /IM specifies the image name, and the /FI option specifies a filter to use, in this case, a user with the username "target_user".

In any case, you'll need to be an Administrator on the local system to forcefully terminate processes in another users security context