There are seven layers, with seven different messages, in the seven colors of the rainbow, hidden in the document Nick gives you. You have to uncover all seven, in any order. Riley will talk and give hints (sort of) as you uncover each message.
Red message:
Sous equino elefant killer, tambor halbbruder estuario
1st slider slightly down from top, 2nd and 3rd all the way down
Orange message:
Savon terra affe respond, ojo family toro.
1st slider slightly down from top, 2nd at center, 3rd all the way down
Yellow message:
Hut ending Nouveau obbligare regalo truthahn heiss.
1st and 2nd sliders all the way up, 3rd all the way down
Green message:
Insano notte turm heaven e huereux offen.
1st slider all the way down, 2nd slightly down from top, 3rd all the way down
Blue message:
Maestro equitativo ordnen far ostr unten rivedere.
1st slider all the way down, 2nd at center, 3rd slightly down from top
Indigo (blue-violet) message:
Garish lieben ovvio respecter Imperiale orange usciere.
1st and 2nd sliders all the way down, 3rd slightly down from top
Purple message:
Schlicht last errore astrologie dunkel essai reason.
1st slider a third of the way down, 2nd all the way down, 3rd all the way up
The solution to the puzzle is "Seek the star of the North in the home of our glorious leader," which is the initial letters of all the words in this order.
But you don't need to know that. Riley solves it for you once you've found all seven messages, and the achievement unlocks as soon as she tells Nick.