The first one is "Black Dragon." It's a mission Notorious Monster. You need to defeat it in order to get to Rank 3, and it is a Lv25 capped fight. I had already defeated this once before, but somebody in my linkshell needed help completing it, so I switched over to my Lv22 Warrior job to help him. I didn't think to get a screen shot the first time I did it, so I took the opportunity to get a screen shot this time. The Black Dragon is one of three different dragons that are involved in the mission to get to Rank 3. I have yet to fight the other two dragons. Maybe some day I will.
Black Dragon

Anyway, my Thief is now up to Lv50. And that means it's time to do the Artifact Armor quests. There are five Artifact Armor (AF) pieces to get. I haven't gotten any yet, but they're acquired through either 1) quests or 2) treasure coffer hunts.
One of the quests involves me going to the Dangruf Wadi and winning three straight gambles with goblins there. In order to get the goblins to show up, I have to trade certain items. Beasts in the area drop those items, so I was killing them to get the items I needed in order to get the goblins to show up. While doing that, I noticed that this NM had appeared. I wasn't even looking for it, but there it was so I went ahead and killed it.
Geyser Lizard

Shortly after I finished the "win gambles with goblins" part of the quest (I still have to fight two quest-related NMs in order to actually get the AF piece), the game server went down for maintenance. When it came back, I decided to try camping the elusive Leaping Lizzy as the server was mostly still empty.
Well, my plan worked and I finally got to catch Leaping Lizzy and add her to my list.
Leaping Lizzy

Now that I've finally caught Lizzy and got a screen shot, that's it for me. I won't be camping that NM anymore. Too much competition, and I have the boots already anyway.
That's it for now. As I catch more NMs later, I'll be sure to add them to my list.