The core of the prayer in the first chapter of Ephesians is found in verses 16-18.
Eph. 1:16: "I have not stopped giving thanks for you, remembering you in my prayers" - Paul also began his prayer in Col. 1:3 by thanking God for the faith of the recipients of his epistle.
Eph. 1:17: "I keep asking that the God of our Lord Jesus Christ, the glorious Father," - Paul also addressed his prayer in Col. 1:3 to God the Father.
"may give you the Spirit of wisdom and revelation" - The Spirit of wisdom is equivalent to "spiritual wisdom" in Col. 1:9, and revelation refers to "knowledge/understanding of His will" in Col. 1:9.
"so that you may know Him better" - The word "so" is equivalent to "in order that" in Col. 1:9, so it is likely that knowing God better is another way of saying living "a life worthy of the Lord" in Col. 1:9.
Eph. 1:18: "I pray also that the eyes of your heart" - The heart in Scripture refers to the human spirit (2Cor. 1:22, 3:2-3, 4:6, Eph. 3:17, Col. 3:15-16, etc.) and "eyes" refers to the human will (MFW, Matt. 13:14-15).
"may be enlightened" - Enlightenment is akin to edification, which occurs as a believer learns GW (Psa. 119:105), and it is in the same vein as "growing in the knowledge of God" in Col. 1:10.
"in order that you may know the hope to which he has called you" - A main purpose of Paul's prayer and aspect of learning is understanding the hope of heaven and experiencing it in part during one's earthly sojourn.
"the riches of His glorious inheritance in the saints." - Paul compares spiritual blessings to physical wealth and calls them "glorious", as he did the Father in v.17, which indicates that desire for heaven is the proper motivation for wanting salvation.
At this point Paul's prayer segues into discussion of God's power, so next let us look at his prayer in Phi. 1:3-11.