She possess a can do attitude.

Is this sentence correct?

No. "She" is a singular pronoun, but "possess" is not a singular verb form.

Would you say this? She walk to the store.

Fix the verb and let me know what you think it should be.

Also "can-do" needs to be hyphenated.

possesses?

That's right.

Yes, the sentence "She possesses a can-do attitude" is correct.