When I finish a challenge in Early Access, how do I activate another challenge in the same game?

That is the only way to do so right now

You don’t have to go back to Classic Pogo.  When you’re done with the game and you’ve won your badge, click on the HOME button (the little house), and when it asks you if you’re sure you want to quit, click QUIT (because you’re done and you don’t care about your progress).
When you get back to the POGO Home page, find the game (the fastest, easiest way is to scroll down to the RECENTLY PLAYED list…it should be the first one…or you can find it by searching by name (using the magnifying glass), or by dropping down the GAMES menu (but this takes forever).  Click on the game and then click on DETAILS to go to the game’s “home” page.
Once you’re on the game’s “home” page, scroll down so you’ll see GAME INFO and CHALLENGES.  Click on CHALLENGES.  I then go to FEATURED CHALLENGES and usually scroll over to the + sign and click that.  It will take you to CHALLENGE CENTRAL…but only for the particular game you’re looking at..scroll down again, and here, you’ll find that you can find all kinds of badges and sort them by the type.  Activate whatever badge(s) you want and then click on the “play” button to go back into the game.
You can also get to this last place by going into CHALLENGE CENTRAL (it’s part of the drop down on the left side of the HOME page under CHALLENGES) and then searching for the game…either way works, but I find going to the game’s “home” page first is faster if I’m looking for a particular game.
Hope that helps.

I agree with Tigger, much easier to go back to Classic and Badge Central!

While I agree that it is easier to go back to Pogo Classic, what happens when Pogo Classic is no longer available?

I’m trying to stay on early access to continue to get more comfortable.  When I finish a game and want to find another badge is same game:
Click on home (little white house)
Click quit
Click Challenge
Browse all  
Use badge finder on left side
Takes just a few seconds to find what i”m looking for.  

The hope is that Challenge Central will be more like Badge Central by then.

It is a pain to have to exit the game to add a new challenge.

Another way is once you click to play game, hit game details.  Scroll down until you see the challenges tab.  That will show you other challenges, new n purchased.
Yes, it is a pain to keep getting out of the game.  Hopefully it will get updated to something similar to what we have now.