She thought she was alone in the hotel gym, so she decided to sing “Eye of the Tiger” at the top of her lungs while exercising. He found it so entertaining, he just had to meet her.
Titles of songs belong inside double quotation marks. (Album titles, like the titles of books, get italicized.) They also get capitalized, according to the same rules as capitalizing any other title, unless officially not capitalized (for the same reason it’s correct to misspell words in the title if that’s how they’re actually spelled: Everyday Is a Winding Road or Nevermind).
There’s a comma in the second sentence because it’s the only way to make it work with the word that left out: He found it so entertaining that he just had to meet her.
(WordPress’ spell check insists gym isn’t a word and wants to change it to Jim. I tell you this only to show how little you can rely on a spell check program by itself.)