Paul recognized that whatever he had become in Christ, whoever he was as a result of knowing Christ, and whatever he did for the cause of Christ was and would always be attributed to the GRACE of GOD. We are not just saved by grace. We also live by God's grace. We needed the undeserved favor of God to save our souls. We couldn't save ourselves. No amount of good works could ever make us acceptable to God. He had to do it all through His Son, and He did all this because He wanted to, not because we deserved it.
Now, the same can be said about our Christian living and Christian ministry. We still need God's grace working in and through us for us to be used of God. We still don't "deserve" God's grace. The very nature of grace is that it is undeserved! And we need God's unmerited favor on us so we can live a life pleasing to Him. Paul made it clear that whatever he did that would be seen as a good ministry, it was God's grace at work in him making him effective in that ministry. Paul knows that in heaven the idea of "no man can boast" is not just talking about salvation. He's also aware that no Christian can boast of their good works as if they did the works themselves. It was God doing the work through the believers.
It should be recognized that whenever Paul wrote his letters he always started with the desire that the believers would be given "grace." He wasn't talking about their salvation but he was talking about their growth in Christ and their ministry for Christ. We still need God's grace every day! Thank God that He is a Gracious God!