Other people had the same problem with the trove's goal, it is a known issue, check the thread about the update. You should send a mail to team lava (support@teamlava.com) to have them solve this for you.
As for the badges, some people focus on one or two until they get them, then they move on. Others play the way they used to (doing different stuff daily), those would get all of the badges at the same time