In Acts 2:38, "for the remission of sins" does not refer back to both clauses, "you all repent" and "each one of you be baptized," but refers only to the first. Peter is saying "repent unto the remission of your sins," the same as in Acts 3:19. The clause "each one of you be baptized" is parenthetical.
Acts 3:19 - Repent therefore and be converted, that your sins may be blotted out, so that times of refreshing may come from the presence of the Lord. *What happened to baptism?
Acts 10:43 - To Him all the prophets witness that, through His name, whoever believes in Him will receive remission of sins. 44 While Peter was still speaking these words, the Holy Spirit fell upon all those who heard the word. 45 And those of the circumcision who believed were astonished, as many as came with Peter, because the gift of the Holy Spirit had been poured out on the Gentiles also. 46 For they heard them speak with tongues and magnify God. Then Peter answered, 47 "Can anyone forbid water, that these should not be baptized who have received the Holy Spirit just as we have?" *What happened to baptism in verse 43?
Acts 11:17 - If therefore God gave them the same gift as He gave us when we believed on the Lord Jesus Christ, (compare with Acts 16:31 - Believe on the Lord Jesus Christ and you will be saved) who was I that I could withstand God?" 18 When they heard these things they became silent; and they glorified God, saying, "Then God has also granted to the Gentiles repentance unto life. *What happened to baptism?
Acts 15:8,9 - So God, who knows the heart, acknowledged them by giving them the Holy Spirit, just as He did to us, and made no distinction between us and them, purifying their hearts by faith. *What happened to baptism?
Faith in Jesus Christ "implied in genuine repentance" (rather than water baptism) brings the remission of sins and the gift of the Holy Spirit (Acts 2:38; 3:19; 10:43-47; 11:17,18; 15:8,9; 16:31). *Perfect Harmony*