Act 2:25 For David speaketh concerning him, I foresaw the Lord always before my face, for he is on my right hand, that I should not be moved:
Act 2:29 Men [and] brethren, let me freely speak unto you of the patriarch David, that he is both dead and buried, and his sepulcher is with us unto this day.
Act 2:31 He seeing this before spake of the resurrection of Christ, that his soul was not left in hell, neither his flesh did see corruption.
Act 2:34 For David is not ascended into the heavens: but he saith himself, The LORD said unto my Lord, Sit thou on my right hand,
Act 2:35 Until I make thy foes thy footstool.
As you can see Peter is referring to the physical resurrection of the body, no where the soul of the believer is.
Twice during the sermon Peter mentions that god promised not to leave Jesus soul in hell along with not letting His body suffer corruption. but he says David’s body is still in the grave to that day and he, David, has not ascended into the heavens. He is not just referring to the bodily resurrection but the whole man body and soul and he is saying that David has not ascended, body or soul., otherwise why is it necessary to mention soul if all that was needed was to affirm by the witnesses that Jesus was raised bodily and ascended bodily?
Acts 2:27, “Because thou wilt not leave my soul in hell, neither wilt thou suffer thine Holy One to see corruption.”
Act 2:31, “He seeing this before spake of the resurrection of Christ, that his soul was not left in hell, neither his flesh did see corruption.”