Working 8 hr shifts in a security position, Is it legal for a company to require that you give up all breaks

When my mother first started this job she was in a booth at night watching a building. She was told that the job required her to sign a contract agreeing to give up all breaks. Since then she has started working days and has no booth and is required to walk a parking lot. They have told her it is okay to bring a folding chair to sit but, she has little time to. Un related, she has been experiencing heart problems and she has missed 2-3 days of work. They wrote her up for this! I think they should be giving her breaks.

California

Most states have laws requiring a lunch break, but very few states have laws mandating any breaks beyond that. You fail to mention what state is involved. If your state requires breaks, she can not be obligated to give up her right to breaks.
If you click EDIT and then ADD DETAILS to mention your state, we can provide a more specific answer.
UPDATE: Thank you for providing the state. Labor Code Section 512 requires a 30 minute lunch break if the employee is working more than 6 hours, but less than 10 hours. This break period can be waived by mutual consent. An employee can not be required to waive it.
In addition, the employee is required to receive a ten minute rest period for every 4 hours worked. This would be two 10-minute breaks for an 8 hour shift. These break periods must be paid and they can not be waived.

Find a local human right or employment lawyer in your state to get competent information .

I'm pretty sure employers are required to give breaks, at least one 30 minute break for every 6 hours and two fifteen minute breaks.