This is a lightweight mod that will let you set an objective for your lobby, similar to Achievement Hunter. If you're hosting a lobby, you can go to the achievements, click on the one you want to set as objective and select "Set as Objective" on the bottom left. A message will appear in chat stating the name and description of the achievement for all players in the lobby. Players that join the game later will automatically get the message once they joined so they know what you're trying to do.

You can also find this mod on GitHub, so if you want to help with anything, feel free to fork the project, make changes and create a pull request when you're done.