Honestly, if you’re not a paleontologist junky — don’t go. Otherwise you will waste your precious time and money.
What Museum of Natural History in Ulaanbaatar can offer you are grotesquely stuffed animals and a few showcases, that look like ones I remember from biological laboratory in elementary school.
Of course there are skeletons of dinosaurs too. These ought to be the greatest attraction here due to many important excavations conducted in Mongolia. They are the greatest, but only in a matter of size. One room with gigantic t-Rex is a bit too little to investin regular ticket.