But what does this highest type of love look like?
What I have been taught is that this can be summed up precisely and concisely:
Agape is the sovereign preference of one above self and others.
It is a process. Like faith, it is not merely a state of mind without commensurate action. The epitome of it is Jesus as both man and God, by His Own obedient will on the Cross at The Father's expense in the place of undeserving mankind.
"Greater love hath no man than this, that a man lay down his life for his friends" (Jn. 15:13 AV), said Jesus of agape on the eve of His crucifixion.
(Treating it as "Christian love" has some exegetical merit, but translating it so is eisegesis, not a precise rendering. Someone can earn a commendation for valor without being Christ or a Christian.)