Why does Superbrothers: Sword & Sworcery ask for your Twitter Password

According to this post, "In sworcery mode left click and hold down on a lagomorph for a few seconds and it should explode"

According to this video guide, you don't need to go anywhere new to find the lagomorphs that you need to kill. The two lagomorphs you indicated are all that need to be found in order to complete this achievement as they can be respawned by leaving and returning to the area. The process is very simple:

1. Kill both lagomorphs.
2. Exit to another screen and return to see the bunnies respawned.
3. Kill both lagomorphs. You will get a message after the first.
4. Exit to another screen and return to see the bunnies respawned.
5. Kill both lagomorphs.
6. Exit to another screen and return to see the bunnies respawned.
7. Kill one more lagomorph. You will get a message.
8. You could try waiting and see if it pops, but in the video guide, although the poster was unsure if it is needed, they exited to the main menu and that's when the achievement appeared for them so it may be necessary to exit to the main menu once the killing is complete.

It lasts the same length as the specific moon phase lasts in real life give or take a bit of approximation by the game. The average lunar cycle lasts about 29.5 days and there are considered to be 8 main moon phases, new, waxing crescent, first quarter, waxing gibbous, full, waning gibbous, last quarter, and waning crescent. While not precise because some phases last slightly different durations than others depending on the positions of the moon, the earth, the sun, and the person observing the moon, rather than complicated astronomical math, a simple approximation is about 3.7 days/phase or so (29.5 days/8 phases). See any site on lunar phases and the lunar calendar that you like, but for simplicity, here's the relevant source information on the wikipedia article.

I'm not sure if the game factors in eclipses.

You can temporarily change the moon phase in the game if you'd rather not wait by going to

the moon grotto

or you can just change your system date if you don't care about only getting 99% completion.