No. I would do that. DACA will not make you eligible either. You might be eligible for instate tuition rate in some states with DACA but not financial aid.
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Because you are on TPS, you are not eligible to apply for DACA. In order to qualify for DACA you must demonstrate that you currently have no immigration status and that you were not in any lawful status on June 15, 2012.
I agree with my colleagues, you should not apply for DACA. Your TPS status is similar and may even be better. DACA will not help you get financial aid.
Gabriela M. Lopez