If you haven't already done this, start by heading to the side mission's waypoint. We've outlined this already in our Phantom Armor guide, but the book points you towards a few collectible clothing items.
For Midna's Helmet, it reads:
"The princess of twilight, whose stories are handed down alongside those of the Hero of Twilight... Her helmet can be found at the temple ruins soaked in the waters of Regencia River."
Regencia River is long: on the map, it runs along the left side of the castle and down. The specific point you need to head to is the Sage Temple Ruins, just outside the Giant's Forest. It's pretty distinctive on your map, even if you haven't been there before.
Head there, and hunt around. Midna's Helmet is here, but there's plenty more besides.
Two lizalfos patrol the area, so it's a good idea to kill them if you want to explore uninterrupted. They're not the smartest or strongest enemy, so you shouldn't have too much trouble killing them.
There are chests scattered around - this one, inside a destroyed building, holds a valuable opal...
... while one just to the south, hidden in the river, has a silver rupee in it. These are nice, but not what we came for.
The chest with Midna's Helmet in it is well hidden. If you find this sword and shield in the north west of the area, poke around – the debris can block your line of sight of the chest from most angles.
Here's the exact position on the map, if you're struggling. Pull it out with magnesis.
There it is! Midna's Helmet gives you additional resistance against Guardians, which is nice.
Now, onto Majora's Mask. The hint tells us that we're looking for ruins next to Lake Kolomo. Open the map...
... and the ruins should stand out like a sore thumb. Warp to the nearest shrine and head there.
This area is safe during the daytime, with no enemies patrolling. You've got time to search, but it's not as well hidden as Midna's Helmet was anyway.
The chest is right in this nook outside one of the destroyed buildings.
Here's the exact map position, if you need it. Lift it out...