If you're after completing this achievement ASAP, open the spoiler. If you are after enjoying the story without spoiler, just continue playing as you would and this will eventually unlock.
Things might be a little different for you as choices affect how the story goes. *** Spoiler - click to reveal ***Upon entering the mine you will need to fight zombies twice, along with two conversations with Petra. Should not be too difficult, use LT to hit zombies and LS to move or avoid. You do have energy though, which drains with each time you use the sword.
After that, you will run into the mine. Use LS and RS to move. First tap 
once or twice, then press 
to grab the cake. Finally, press 
to avoid the explosion.
Then 
.
Then it is back to running. , slash some of the spiders which attack you, then to jump over the lava. After that, you can choose to either help out Petra or win the race.
Faster option is winning the race ( Tap a few times to jump over the lava. )
Helping out Petra will result in fighting off some spiders, and then removing the gravel brick with LS + .
You will find a llama, try to ride him and he will eventually escape. You will need to craft a torch. Place a stick in the middle bottom spot and some coal in the middle spot on the middle row.
Then to grab the torch. Take down the llama to reveal a new room. Upon receiving the prismarine glove the chapter is finished and your achievement will pop.