Paul says what will bring him joy is the church being of the same mind, having the same love, united spirit, and having one purpose.
That seems like a tall order. I mean different people having the same mind, love, united in spirit (attitude), and one purpose!
Same mind
In the next verses, Paul will tell us that the basis of our being united, being of the same mind, is Christ. With the focus on Christ, the humility of Christ, we can be of the same mind. I actually see this as possible and being made possible by the Holy Spirit.
Before his death, Jesus promised the Holy Spirit. He said he is the Spirit of truth (John 14:17, 15:26, and 16:13), the Spirit that will glorify him (John 16:14), the same that would take of what is His and manifest it to us. So with that, with having the same Holy Spirit, we can have the same mind.
Same Love
The four things Paul mentioned in this verse can be regarded as the four sides of a square. There is a connection between having the same mind, love, spirit, and purpose. It starts with the same mind, how you are thinking about things, the facts available to you, then we have the the same love, which is the direction of our affection, which is clearly connected to our thinking (same mind), and then we have united in spirit which is the direction of our action, and then there is one purpose, meaning the end point we are aiming for.
We can clearly recognize the idealism in the words of Paul here, but it is not different from the prayer of Jesus.
I am not praying only on their behalf, but also on behalf of those who believe in me through their testimony, that they will all be one, just as you, Father, are in me and I am in you. I pray that they will be in us, so that the world will believe that you sent me. The glory you gave to me I have given to them, that they may be one just as we are one— I in them and you in me—that they may be completely one, so that the world will know that you sent me, and you have loved them just as you have loved me. (John 17:20-23)
We are one because we believe in the one Christ, we are one because we have one Christ in us, and we are one because of the shared sense of love for the Father and in the Father.
Jesus prayed it, and Paul is saying people should work at it.
So my thesis is that the Holy Spirit is the one who brings this to pass. For example, we read in Romans 5:5 that the love of God has been poured out in our hearts by the Spirit he has given to us, which means our affection is in one direction- God. Also in 1 John 2:15-16, John mentioned the need for us to have the love of the Father in us (John 14:31). That is the same love that was in Jesus. So whatever Paul was aiming for in this verse, it is not achieved by mental exertion, but rather by the Holy Spirit. Zechariah 4:6 says, It's not by power, nor by might, but by my spirit says the Lord.
United in spirit
It means pulling in the same direction. It's about the effort we are making. Every Christian is meant to make the effort for the cause of Christ. But sometimes we are too judgmental of differences in approach and presentation. But when someone was casting out devils in the name of Jesus, the disciples wanted Jesus to stop them (Mark 9:39-40). Jesus said the one who is not against them is for them.
Having one purpose
Jesus said that oneness among the believers would be a sign that Jesus is the truly sent one (John 17:21-23). But a shared purpose that is not based on the same mind, same love, and united in spirit is suspect. It is like the seed that falls in a rocky place that does not have a deep root.
Complete my joy
Paul is saying this is what will make me really happy. "The gift you send me is good, but this is what will really make me happy." John said something similar.
I rejoiced greatly because I have found some of your children living according to the truth, just as the Father commanded us. (2 John 1:4)
For I rejoiced greatly when the brothers came and testified to your truth, just as you are living according to the truth.
4 I have no greater joy than this: to hear that my children are living according to the truth. (3 John 1:3-4)