This can be done in Chapter 3. The Beta spot is at 19,7.
Go to 22,7 first and drop down in the hole. Grab the yellow power up and go back up. On your left there’s a small brown plant. Position yourself here and activate the power up (L1). This will shoot you up vertically. You’ll get to a path all the way at the top. Follow the path to the room on your left. You’ll see a diagonal ramp below. You’ll have to fall down and turn into a ball (X) and aim for the ledge on the left. Now go up and follow the path all the way to the left room (18,7). Grab the wall on the left and go down to the room below and you’ll see the Beta icon on your left. Now remember how this room looks and go back up to the previous room. While holding the ledge, turn into a ball and use your speed boost (R1). Once you hit the floor at the room below, you’ll have to aim towards the Beta icon and grab the ledge.
Credit to: http://www.ps3trophies.org/game/knytt-underground/guide/
Credit to Mr Vuule for the video