If you want to gain the power to open the vault with the calendar piece, Diggy has to perform a ritual in the Temple of Restoration. Let's get there quickly.
Do not worry, Mama Quilla said she'll help you with it but first of all Diggy needs to ask the following villager if he's seen her.

Something bad must have happened to Mama Quilla. You will find signs of struggle. Diggy has to figure out what happened here and find her. She could be in real danger. Please enter the following portal to another dimension:

Since Viracocha abducted Inti's beloved sister, Diggy needs to save her. Without her help, Diggy can't perform the ritual. Now, let's unlock the bridge with the blue buttons. As shown in the picture below, each button unlocks the following set of bridges:

Push the following button in order to proceed to the exit:

If you want to save Mama Quilla, Diggy has to destroy three green crystals. Their power is keeping her imprisoned.
In order to destroy green crystals, Diggy needs to unlock the way with the help of buttons. Here is the correct setup for each crystal:
crystal on the LEFT side
crystal in the MIDDLE
crystal on the RIGHT side
Great Diggy. Now let's go to the Temple of Restoration to perform the ritual. With it, Inti will get back the power to open the vault with the stolen piece of the calendar.
To open the way to the ritual chamber, please ignite the braziers near Mama Quilla's statues.

They'll transform it into the moonlight that will open the way.

In order to proceed, Diggy needs to light up the six Inti's golden statues which contain power that unleashes only after a touch of moonlight. Please note that during this puzzle you will need to light up the four blue receivers.

GOLDEN STATUES
1st golden statue
2nd golden statue
3rd golden statue
4th golden statue
5th golden statue
6th golden statue
BLUE RECEIVERS
1st blue receiver
2nd blue receiver
3rd blue receiver
4th blue receiver
YELLOW RECEIVERS
Excellent! We can proceed to the ritual chamber. Please aim the rays at the statues and the ritual will begin!