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 ***
Start by walking to the other end of the room. After some conversation and walking you will need to put your glove into a hole again. Then, there are 2 elder guardians in the next room. Be ready to press 
. Look at the Elder guardian and the sponges. You can dry up the floating water with the sponges. Choose either to distract the elder guardians (
) or to place the sponges (
).
If you like me chose to distract the elder guardians you will need to press 
. Catch the sponge with LS + 
, then press to place the sponge and to kill the 2nd elder guardian.
If you chose to place the sponges, tap A , throw the sponge at the elder guardian with LS + and then finish him with A. Tap A again, throw the 2nd sponge and then kill the 2nd guardian with A.
Head to the back of the room, taking the guardian loot on your way. Open the chest and then use the crafting table to craft a Sea lantern (fill the corners with prismarine shards and fill the rest with prismarine crystals. You will need to create 2 of them.
Then investigate the puzzle door and place 3 Dark prismarine blocks and 2 sea lanterns so that they are symmetrical (from top to bottom it is Dark Prismarine, Sea lantern x2 and Dark prismarine x2. Upon that the door will open and you will meet Vos, one of Jack's friends.
Place your glove in the hole once more. You will barely escape zombie like creatures and enter up in another room. Keep going up the stairs, Nurm will translate the runes for you, go up even further and you will find the structure blocks.
You will need to chose between the builder path (right hand side block) or the warriors path (left hand side block) Personally I went for the builder path, but either way, your achievement a Gift from the deep will unlock.