You can discover Elementals while exploring the world. The more you level up through completing your quests (or idling), the more locations you unlock. So you'll get access to more Elementals as you go. Some of them are very easy to spot. Some are hiding a little. Some aren't always there. I've found most of them pretty straightforward so far, but I know that not everyone has good eyesight for one thing.

I think it can be fun to try and discover them yourself, so I'm offering the level number and a hint for each of them first. Note that the level number is already a hint in itself, so I'm putting them all in spoiler tags and letting you decide for yourself how much you'd like to see :)

I've sorted them from lowest to highest level - so you can easily check if you've missed one!

Update: I've added a short overview of the achievements below, and a section with info on progression - XP, coins, location unlocks - for those who've been wondering.

accessible from: level 1
hint: likes bringing a bit of forest into towns
how to find them: at Oltak Cafe, in the moss on the wall
pic that totally spoils the location:

accessible from: level 4
hint: not really necessary judging from global achievements, also featured on the store page (:
how to find them: at the Shadow Lake, among the bits of dead wood on the beach
pic just because it's cute:

accessible from: level 7
hint: the name is a strong hint already, but this one is a bit more complicated (:
how to find them: at the Campfire, only in daylight and while it's not raining
cute spoiler pic:

accessible from: level 10
hint: it's looking at you with an underwhelming amount of eyes
how to find them: in the Secret Forest, next to the big overgrown stone tablet
pic in their natural habitat:

accessible from: level 13
hint: location should be straightforward once you reach the level, but you might have to take a closer look
how to find them: in the Autumn Forest, between fallen leaves in the right half of the picture
pic in their natural habitat:

accessible from: level 16
hint: I "found" it accidentally :(( but I guess that's a hint, too...
how to find them: in the Forest Walk. It popped up for me when I was just trying to hide the UI :(( so it must have been at that height at least

accessible from: level 19
hint: likes water and is very old
how to find them: At the Blue Lake (the one further East), in the shallow water to the left.
pic in their natural habitat:

accessible from: level 22
hint: loves hiding in ancient things
how to find them: At the Sea Temple, in an ancient helmet (?) between the rocks and the former temple floor.
pic in their natural habitat:

accessible from: level 27
hint: yes, the name makes it pretty obvious once you've unlocked the location
how to find them: At the Mountain Pass, sticking out of the snow in front of the left side of the building.
pic in their natural habitat:

accessible from: level 29
hint: it's in a very high level location and you pretty much can't miss it once you get there
how to find them: At the Beach, the western one that's the last to unlock for now. Hovering right in the middle in plain sight.
pic in their natural habitat:

These are all very straightforward. Now there's a bunch of people using this game/tool who might not be very familiar with Steam, and the game library view shows some of them as "hidden"... So just for the record I'm going to give a little overview here:

Activity-related
- Welcome to Oltak: You arrived in Oltak to start your studies.
I'm pretty sure you can figure this one out, but if this is your first day using any kind of program then there's an incredibly helpful guide for it...
- First Task Done! You completed your first task. By "task", they mean quest of course (:
- First Timer Complete! You completed your first timer. The symbol should have been an hourglass rather than a stopwatch, I guess?

Progression-related:
- Mage Apprentice: You reached level 5.
- Master Mage: You reached level 20.
- Grand Master Mage: You reached level 50.
If you're wondering about levels, scroll down to the last section.

Elementals:
The remaining 10 achievements are for discovering Elementals. They are listed in the index here (:

For those that are earlier in the game/tool and wondering about how progression works, when they'll be able to afford that nice outfit or decoration, maybe which locations to look forward to... I thought I'll share what I've figured out.
Update May 14: XP amounts were adjusted, and added for the habit tracker.

This will get you XP to level up:
- daily log in +100
- 1st daily quest or habit completed +80
- 2nd daily quest or habit completed +70
- 3rd daily quest or habit completed +60, etc.
- ...8th daily quest or habit completed +10
- 9th+ daily quest or habit completed +5
- timer completed: depends, see discussion with @Sly BluePaw and @sir_lami below
...TL;DR you get a good chunk of XP for timers of 10+ minutes
- discovering a new Elemental +250
- every minute spent in-game +5 (can be turned off in the advanced options now)

So from what I've figured out, quests and habits have the same XP pool now. You'll get progressively less daily XP from them until you end up with +5. There's no difference in XP for main and side quests. If you spend time with Ithya in any way, it'll add up.

The amount of XP you need to reach the next level is the current level x100, up until level 10. Beyond level 10, you'll keep needing 1,000 for each one.

You might wonder about the cash for decorations: While you'll need more XP at higher levels, thankfully you'll also get some more of those precious silver coins. Your first level up will only net you 2 of them, but after that it's 4 for level 3 to 9. Starting from level 10, you'll gain 10 coins per level.

XP needed, coins gained and locations unlocked for quick reference:

level 1->2: 100 XP required; +2 silver coins, new location: Oltak Outside
level 2->3: 200 XP required; +4 silver coins, new location: Oltak River
level 3->4: 300 XP required; +4 silver coins, new location: Shadow Lake
level 4->5: 400 XP required; +4 silver coins, new location: Tavern Study
level 5->6: 500 XP required; +4 silver coins, new location: Oltak Library
level 6->7: 600 XP required; +4 silver coins, new location: Campfire
level 7->8: 700 XP required; +4 silver coins, new location: Mountain River
level 8->9: 800 XP required; +4 silver coins, new location: Valley
level 9->10: 900 XP required; +10 silver coins, new location: Secret Forest

level 10->11: 1,000 XP required; +10 silver coins, new location: River Swim
level 11->12: 1,000 XP required; +10 silver coins, new location: Valley (a different one)
level 12->13: 1,000 XP required; +10 silver coins, new location: Autumn Forest
level 13->14: 1,000 XP required; +10 silver coins, new location: Beach
level 14->15: 1,000 XP required; +10 silver coins, new location: Mountain Valley
level 15->16: 1,000 XP required; +10 silver coins, new location: Forest Walk
level 16->17: 1,000 XP required; +10 silver coins, new location: Forest River
level 17->18: 1,000 XP required; +10 silver coins, new location: Blue Lake
level 18->19: 1,000 XP required; +10 silver coins, new location: Blue Lake (another one)
level 19->20: 1,000 XP required; +10 silver coins, new location: Blue Lake (yes, another one)

level 20->21: 1,000 XP required; +10 silver coins, new location: Dungeon
level 21->22: 1,000 XP required; +10 silver coins, new location: Sea Temple
level 22->23: 1,000 XP required; +10 silver coins, new location: Swim
level 23->24: 1,000 XP required; +10 silver coins, new location: Lissos Coast
level 24->25: 1,000 XP required; +10 silver coins, new location: Lissos Tavern
level 25->26: 1,000 XP required; +10 silver coins, new location: Lissos Tavern Inside
level 26->27: 1,000 XP required; +10 silver coins, new location: Mountain Pass
level 27->28: 1,000 XP required; +10 silver coins, new location: Lavia
level 28->29: 1,000 XP required; +10 silver coins, new location: Beach (another one)
level 29->30: 1,000 XP required; +10 silver coins, new location: Campfire (another one)
level 30->31: 1,000 XP required; +10 silver coins, new location: Blue Lake (ANOTHER one)
level 31->32: 1,000 XP required; +10 silver coins, new location: Blue Lake (aaand another one!)

That's it for now! All locations unlocked, looks like XP and coins are staying the same.

Just in case anyone else is tempted to reset their game (which you can do in the advanced options menu) and would appreciate this info:
It will not only reset all your in-game progress, but also all your achievements. So you can't clear those first and then do a second "playthrough" where you keep the Elementals in their natural habitats. Oops (:

I'd be happy to know if this was helpful, or if there's anything else you're wondering about!

Please correct me if I'm wrong somewhere (if there are extra conditions required that I happened to have), or confirm my "?"s if you can. Don't reveal any info without using spoiler tags, though!

I hope everyone is enjoying their stay in Oltak <3