Confirm your first map. Confirming maps involves going to a peak, and then from the view, scrolling until you find the place that matches the map in question, marking it, and then going to that marked location, opening your journal, and if you're in the right spot, Moira will confirm the map and it will get a check mark in your journal. You'll need to do this a LOT to unlock paths and items.

Climb your first peak. You will do this in the tutorial.

Complete a flawless run - this means doing a sprint section and hitting every jump. If you're having trouble with this, check out the accessibility options in the settings - you can opt to use just one jump button instead of two, or to use simpler musical rhythms. (You can also set it so Moira trips less, but if you trip even once you're not going to get the achievement for that segment anyway.)

Confirm 3 maps.

Find a goshawk. Goshawks are scattered all over, usually perched somewhere slightly hard to get to, and you have to disturb them - walk up to them, throw a stone at them, etc - to get them to fly off, which will trigger a memory for Moira.

Climb 5 peaks.

Confirm 5 maps.

Correctly name 5 peaks. So this means not just assigning the correct name to the peak, but confirming the name by matching it up to a map. Not all maps mention the name of the peak in the picture, so you may have confirmed maps that show the peak that still don't confirm the name. You can also sometimes identify a peak based on something Hamish tells you. You'll know you have confirmed the name if it no longer has a question mark beside it in your journal. If you're having trouble finding a map for the peak, try looking around nearby - some maps are only found in specific locations, usually close to the area they affect. You can also try assigning a name to the peak, and then going back in and choosing "That sounds right" or "I'm sure that's it" and sometimes Moira will remember that Hamish mailed her a map earlier involving this peak. (Girl, why wasn't that already in your journal!)

Climb 10 peaks. This does not have to be all in the same run!

Find 3 goshawks

Reach the lighthouse, at all, doesn't matter if you're 50 days late.

Reach the lighthouse just after beltane. If you arrive the day after beltane, Hamish will take you to the cliffs, but you can't go down to the water. I got this achievement when I arrived late in the day on beltane itself, so it seems to have some flexibility. I'm not sure how long after beltane still counts - drop a comment if you get this achievement later than 1 day after.

Confirmed 10 maps

Correctly named 10 peaks. See the Student achievement for details about what counts for this.

Meet the spelunker. He is in the caves under the Hogshead / Togsaid. If you get to the glittery room, jump up on the boulders and then go left to reach his... uh... throne room.

Find 5 goshawks

Reach the lighthouse for beltane. Arrive any time on beltane, or on an earlier day.

Meet the ice climber, who is in a cave on the left side of Broken Tooth. If you die from a fall in the area (including on Witches' Peak and Sharpstone,) you may wake up in his cave.

Correctly name 15 peaks. See the Student achievement for details about what counts for this.

Get an eagle to carry you off! This is done on Eagle's Nest (surprise) - pick up the Massive Quartz Rock, which is near the peak, and place it on the peak. An eagle will promptly show up and cart you off to the next layer.

Confirm 20 maps. See the Student achievement for details about what counts for this.

Met the giant. He is in the crofter's village below Hope's Ladder. To get the achievement you need to talk to him. He can't hear you from way up there, so you either need to find the Dented Megaphone and use that to talk to him, or climb up to a spot nearer his ear to talk to him.

Correctly name 20 peaks. See the Student achievement for details about what counts for this.

Climb 25 different peaks

Confirm 30 maps. There are 91 maps in the game, so this will probably happen naturally in the course of playing.

Find 10 goshawks

Meet the ghost of a soldier. If you sleep under the tree on the peak of Lovers' Leap, the ghost (a Jacobite soldier) will visit you that night. Note: if you have met the pilot, that is not the character that counts for this achievement, even though he is also a soldier.

Hear the fisherman's tale in full. You get a scrap of the tale every time you bless a peak, die, and sometimes when you sleep, so you will probably hear it all within a couple of runs.

Find 15 goshawks. There are 20 in the game. I'm working on a goshawk guide, but haven't found them all yet!

Reach the lighthouse within 3 days. This is probably not possible on a first run - you will want to unlock a lot of maps with short-cuts first.

Complete the King / Blue Man's quest. The King is lying on the ground in a bush in the sunken village between Forest Crown and Devil's Tail. Just talking to him isn't enough. First you need to find the injured crow on Outer Wall, feed it, then follow it (a new path is opened by helping the crow) to the next area, and after interacting with it there, you will be given an object. Give this object to the King and he will wake up and talk to you, netting you the achievement.

Make a wish at the wishing well, which is located under Golden Field. First you need to "wake up" the well spirit by tossing in at golden items. The easiest way to do this is to get the barley grain from the roof of the barrel warehouse nearby - you need something to pry the barrel open, like the crowbar. You can throw in barley twice and the well will awake. (Otherwise, you will need to throw in four golden items - golden necklace, golden brooch, golden wedding band, gold flower. This can be over multiple runs so you can use some of the items twice.) Once this is done, the well spirit will wake up and talk to you. Some conversation forks lead to you making a wish. If you finish the conversation without getting the achievement, you can throw in more barley (you get six grains in your handful, and if you run out you can go get another handful from the barrel) to wake up the spirit again to keep talking and choose a different conversation option to try to get a wish. The golden brooch can be found in the hearth of the cabin on Warrior's Walk, the golden necklace is in a little ravine between Bald Edge and Giant's Tooth, the gold wedding band is in a hidden cave on the left side of the PIllars. The gold flower is found by leaving a gold item on Golden Field.

Climb all 36 peaks in the game.

Correctly name (and confirm) all 36 peaks. See the Student achievement for details about what counts for this.

Arrive at the lighthouse without sleeping, ie, before dawn of the next day.

One possible route: take the shortcut to the jetty near Gull's Perch, take the boat (the Raspberry) to Stonesong, enter the cave to the right and ascend, hop up to the level the deer is at, run left with the deer, drop down halfway on to the little area with a small cave, take the cave to the unnamed ruins, exit that cave and climb up the ruins, then walk left and take the path by the cairn to Crofter's Echo, take the Crofter's Echo cave to Eagle's Nest, use the 3 sisters path under the bridge to get to the end section. After using the 3 sisters path, be careful to hop up on to the middle path where the deer is, don't just walk right on to the lower path and jump up, because you will fall asleep as soon as you're off the "right" pathway. If you stick to the one level the deer is on, you will stay awake through the sprint and then you can't fall asleep on the Lighthouse causeway.

You'll notice to need to unlock a LOT of maps to make this work - this is a tricky achievement to get! If you search for Highland Song speedruns, the NG+ record has a video of someone doing this successfully.

Bless all 36 peaks. See the separate Blessings guide for details on how to do this if you get stuck.