From the comments, it looks like you understand what the phrase means - that the person has accomplished a life goal, or seen something that they hoped for realised in their lifetime. I assume that you are looking for other 'well-known' phrases for the same situation.
Interestingly, as much of a cliche as this phrase is, it doesn't seem to be something people actually say on their deathbeds. I looked at a few references on "famous last words" here, here and here, and I was surprised to see that none of them were even similar to "now I can die in peace". It seems such a well-known, cliche phrase I felt it surely must have been somebody's dying words. Actually, in real life, it is probably said more glibly, not by people who may actually be dying (at least by no one notable). I've certainly heard people say it sarcastically, in response to something underwhelming.
Really then, I'd have to say there are no phrases that mean exactly this because you couldn't achieve the melodrama of equating something with dying satisfied without actually mentioning death.
If you simply want to state that someone has accomplished their life's ambitions you could take your pick from any number of other cliches:
I have reached all my goals.
All of my dreams have come true.
I have accomplished everything I set out to do.
I am living the life I always wanted.
I am living my best life.
Context is everything, but as a word of caution - the more 'sincere' you make a declaration of accomplishing all your goals, the more 'insincere' it can sound to others. It could be seen as bragging, exaggeration, or over-confidence to say that you have achieved everything in life you wanted to, especially when you have more of your life yet to come.