If my Tuition fee was paid a 100% by my ER and it is not included in box 40 of my T4, Do I still need to fill out the T2022-A?

The educational institution fills out the T2202A for you if you are able to claim any tuition fees.  Since the tuition fees were paid 100% by the ER, you cannot claim these fees as tuition fees.  You do not fill out the T2202A yourself and in your case you are not able to claim the tuition fees reimbursed or paid to you by your employer unless they included it in your income as taxable benefits.