Are dungeon boss characters random?

I remember in the Ikki dungeon (level 30 one) I once fought this snake thing. But I didn't get achievement. And since then I have probably done this dungeon 20+ times and NEVER seen that snake again.
The same dungeon, there is sometimes a green arrow near the cliff after the random Black Andromeda spawn. There is an NPC crying for help at the bottom of the cliff. How do you save him?

Another achievement is in the 12 house Cancer>Leo>Virgo. I have never seen any bonus boss but it's there in the achievements. Has anyone encountered him?

The boss is random. When you arrive in that area, there is a chance to encounter Andromeda, Snake boss (yes, it's rare but not impossible) or the man to help.
To help the man, jump into the abyss to reach his location; if you have an Andromeda class in party, heal him. After that, he will become a vendor (nothing special).

Is it possible to miss the snake boss? If I recall, it appears in the room just before Black Dragon?

Yes.
It randomly appear in the room before Black Dragon (the one where randomly appears Black Andromeda). if it appears, it's difficult to miss it because there will be a warp that teleports you over a rock. You can jump over the rock even without the warp, but the snake boss appears only if there is the warp.
I think that the probability is 1/10 - 1/20.