I currently thought I would set the db up like this
Employee Info(id,first,last,staff/hourly,department,job description
Then a tables for each department(20) with there required training. Also a general training table.
So each table would have columns with there training and a date of completion record.
I think Your suggestion will make it much easier and faster. I think I am still going to keep a table for each department. It should make it easier to find each departments requirements.