Dice Tribes: Ambitions has a number of secret ambitions that are not available when selecting a scenario. They are revealed in the achievement list both on Steam and in-game, so their existence and names aren't particularly hidden. The Compendium also lists them, as well as what to do to finish them.

What isn't listed, however, is the method of triggering these ambitions; this guide will cover those. Obviously, this is spoiler territory for things that are meant to be secrets.

Do remember that since you cannot change ambitions, if you have already chosen an ambition you will not be able to complete a secret one, though you may see its events if you trigger them. Therefore, if you are actively targeting a secret ambition (to get the corresponding achievement), you need to not take one of the other options.

Use an Explorer to start an exploration in Forest or Hills, but after you start a deep exploration, use Doctors every time. Eventually you'll get an "Ancient Forest" location that starts the Ambition.

Most easily done with the Archaeology scenario, as it starts you with both an Explorer and a Doctor, the ability to force them to 6s, and Forest as an explorable location.

To trigger this one, just survive for long enough, which will cause the "At Death's Door" event to spawn, then place a dice in the Any slot on it to start the event.

This is most easily done with the Fishing Village start, as you can get First Aid Training, the Medicine research, and also the Waterfall unique location; both Doctors and Researchers have lots of 5s on their dice. You can also build an Altar for Divination, which further helps.

You ARE able to pick this ambition even if you already have one selected. It will replace your current one.

To trigger the Rat King ambition, wait until the Rats event appears, then simply let the rats populate. After they reach the maximum of 5 rats, they will turn into the Rat King danger, which has an Any slot to allow you to start the corresponding Ambition.

This does not seem to always trigger without fail by letting the rats reach 5; some further testing is needed. It may be a random chance, possibly per-turn while there are 5 rats.

Easily done on any scenario where food is not a major concern.

To trigger the Lich ambition, you must first let villagers die. I'm not sure exactly how this works, but as far as I can tell from playing, the Ambition has a random chance to show up every turn as long as at least one villager has died. I have seen it show up with exactly 1 total death (due to starvation).

A failed Hunting roll can do this, but carefully managed Starvation is the most practical way to do it if you can have lots of "standby food" to recover from being at zero; traps, apiaries, stocked-up forager huts, and other things where you can leave food in-place until you need it.

Eventually, a "Necronomicon" event will show up on the bottom row, with a single Any slot. Taking it will change your village to a dark temple and allow you to begin the Lich ambition.

The Kraken is found during the Voyage ambition, so you must first take that Ambition, construct a ship as normal, and head out to sea.

Fully explore the map. The Kraken is always found within a circle of Stone Pillar tiles, so you will have to use the Lookout action to find it, and you will have to crash through a stone along the way. This will give you a broken hull event so make sure to be prepared for that.

Stop on its square to begin the Kraken event/ambition.

To give credit where credit is due, I found almost all of these on my own, but had to look for a hint on Immortality, which I found in this thread: https://steamcommunity.com/app/1965800/discussions/0/3418810183124851200/

And also, big thanks to the creator of Dice Tribes: Ambitions for making such a fun little game.