Achaia refers to the region south of Macedonia. During Paul's time, Gallio was the proconsul.
Rom 15:26For Macedonia and Achaia have been pleased to make a contribution for the poor among the saints in Jerusalem.
Acts 18:12But when Gallio was proconsul of Achaia, the Jews made a united attack on Paul and brought him before the tribunal,
Acts 18:27And when Apollos wished to cross to Achaia, the brothers encouraged him and wrote to the disciples to welcome him. When he arrived, he greatly helped those who through grace had believed,
2 Cor 1:1Paul, an apostle of Christ Jesus by the will of God, and Timothy our brother, To the church of God that is in Corinth, with all the saints throughout Achaia:
1 Thess 1:8For not only has the word of the Lord sounded forth from you in Macedonia and Achaia, but your faith in God has gone forth everywhere, so that we need not say anything.