Give this a try,
SELECT e.fname, e.lname
FROM employee e
INNER JOIN emp_education_list l
ON e.skillsID = l.skillsID
INNER JOIN
(
SELECT li.educationID, li.edu_level
FROM emp_education_list li
INNER JOIN job j
ON j.skillsID = li.skillsID
WHERE j.jobID = 1001
) x ON l.educationID = x.educationID
WHERE x.edu_level < l.edu_level