Correct usage with phrases

I grew up in the in the South and it's always been that 'man up' type of attitude, get on with life.

Is the phrase on the end a noun phrase or just a phrase tagged on the end of the sentence?

Any rules with phrases used this way in sentences ?

Native English speaker here.

I feel like "Man up" is often used as an imperative, i.e. "(You) should man up!". I don't think I've ever heard it used as an adjective.

Examples:

"Don't be a weakling. It's time to man up!"

"Helen was having problems running around the track for 30 minutes. It was too much for her. Tonya told her to "Man up!" and then something clicked. Helen tried harder and then, one day, she could run around the track for an entire hour."

man up TFD an idiom

To deal with something in a more brave, stoic, or masculine way than one has done so hitherto. (Usually used imperatively.)

It's just a tiny scratch! You need to man up and quit crying about it.

And get on with (something) TFD is also an idiom

To proceed with some action, intention, or pursuit, especially after a delay, distraction, or pause of some kind.

Thus "Is the phrase on the end a noun phrase or just a phrase tagged on the end of the sentence?" It is just a phrase you have added to your question.