This is an Idiomatic Verb Phrase which comes from the world of the performing arts: Ballet, Theatre, Comedy, etc.. The word, “Act” in this phrase is referring specifically to one’s performance. The Separable Phrasal-Verb, (to) “Get (something) Together”, is in-reference-to making that performance perfected and “in sync” with others involved in the performance.
If One’s “Act” is “Not Together”, then it could be said that his or her performance is not very well organized, and was performed in a sloppy or poor manner.
. Used Idiomatically, the phrase refers to the same situation in any person’s performance – whether it be in school, work, social-life, or even in how a person takes care of him or her Self.
So, in like manner, to say that a person (usually in His or Her job, studies, way of living, or general behavior) needs, “…to get His / Her act together…”, is to say that He or She is doing a really poor job of what-ever it is that He or She is doing – and that He or She needs to make some quick and drastic changes…(or else something “bad”, or at-least, quite un-desirable) may happen.
Have An Excellent Day!
(And Good Luck!)