Agonizomai. This word means to struggle, to wrestle with, to contend or compete with an adversary. In Colossians 1:28-29 we see that Paul labored and struggled (agonizomai) with all the energy of God, which was working (energeo) in him, to admonish and teach everyone with all wisdom, with the goal to present everyone perfect in Christ. So here, whereas some people struggle just with their own personal problems, Paul struggled and worked (with the power of God behind him) in behalf of others.
And we can believe that, as he struggled to admonish and teach, the real struggle was with the devil (Eph. 6:10-13), and his weapon against him was prayer. For this reason, we can say that earnestness in prayer is working and struggling in prayer (by the mighty power of God) against the forces of evil. And we do it with the goal to present people perfect in Christ.
Epaphras, who was one of Paul’s co-workers, was also a good example of one who wrestled in prayer. As Colossians 1:12 tells us, he was always laboring fervently for the Colossian church in prayers, that they would stand perfect and complete in all the will of God. And the reason he labored so fervently for them is because he had “a great zeal,” for them (v. 13). It was zeal of love for them implanted in his heart by God—a zeal that empowered him to be a mighty wrestler (against the devil) in prayer.