What were the Judaizers trying to do to the Gentile believers in the Galatian churches?

The Judaizers were attempting to bring the Gentile believers in the Galatian churches under the law and legalism. Paul wrote to these churches because they were being deluged with Judaizers who tempted them with legalism, seeking to add Jewish legal requirements to their faith.

Les explains that the Judaizers were trying to bring the Gentile believers under the law and legalism. Paul had established Gentile churches in Asia Minor and received word they were being tempted with legalism, so he hurriedly wrote this epistle. The gospel Paul preached among the Gentiles was an advance: God was going to the pagan, idolatrous world to bring reconciliation outside of Judaism, which the Jerusalem believers found incomprehensible. The Judaizers' aim was to impose legalism on these Gentile converts.

Galatians 2:1

Then fourteen years after I went up again to Jerusalem with Barnabas, and took Titus with me also.

What were the Judaizers trying to do to the churches in Asia Minor?

The Judaizers were seeking to bring the Gentile believers in the churches of Asia Minor under the law and into legalism, pressuring them to adopt Judaic legal requirements instead of the grace gospel Paul preached. They deluged those churches with this pressure.