of (one's) life
Used to indicate something that has an extreme impact on one's life, for good or ill. These underdogs are in the fight of their lives to defy expectations and go home with the championship! This has been, without a doubt, the worst vacation of my life. I was fortunate enough to have found the love of my life in high school.
of one's life
Being the greatest, worst, or best occasion of a lifetime, as in She was having the time of her life at the party, or The threatened takeover of the company put the president in the fight of his life.