Does my mother have to file taxes if her only income is social security also she received the first stimulus check but not the second one ?

Yes. She should file to receive the second stimulus check. 

File a tax return with the new Recovery Rebate Credit Worksheet. This will allow you to reconcile your stimulus payments and receive any additional payment (refund).

IRS Recovery Rebate Credit

In TurboTax Online once your return is open, select Wages & Income (to enter the tax return).

Select Federal Review at the top of the page > Continue to answer the questions for Let's make sure you got the right stimulus amount

TurboTax will then include any stimulus amount due on their 1040 form - either added to their refund or it will reduce the amount due.

There is nothing else to put on your return except your personal information.

For more information click the link: Economic Impact Payments for for SS and SSI Recipients