After completing the story of this DLC and going through the end game cutscenes, you will return to your newly acquired home. During this cutscene, Joker will ask you about throwing a party and you can choose whether to throw one or not. Choose the dialogue option to 'Begin party preparations'.
You will then be prompted to purchase party supplies from the Silver Coast casino. Proceed to do this. Then, you will need to invite your companions. To do this, go back to your apartment and using the message terminal you can choose who you want to invite. After inviting who you want, Glyph will ask you what kind of party you want, then after choosing, the party will begin.
You just need to mingle in the party for a while. Glyph will, at intervals, change the atmosphere of the party to your choosing. Then, after taking a group photograph, finishing the party, the achievement will unlock.