LS completion as early as the release days
I’m not sure about the Jubilee pavilion achieves because I haven’t really been back there myself too much (though when I was there browsing items it seemed like bosses were still going down, so perhaps try guesting to a more populated server?), but I don’t agree at all on the Clockwork Chaos achieves.
I still get into Overflow maps at least half of the time for invasions, which shows there’s still plenty of interest. Only one achievement requires actually completing the invasion, so while that one achieve may be getting more problematic, the rest are still viable, and even the Scarlet kill achieve should still be doable eventually (I’ve had about 50/50 success rate on invasions the last couple days).
That said, its always good to get LS stuff done ASAP, or at least start working on it right away. Starting early lets you spread out the more grindy achieves a bit more (so you don’t have to spend hours in a row doing a super repetitive task like breaking piƱatas, you can do a few a day for instance), and in the case of dungeons and stuff its better to get in early so you can be in when people are still learning the dungeon and more accepting of “newbs” rather than waiting until everyone else is experienced and may get more frustrated with new players.
For easiest/quickest way to get achievements, start doing the content the second day it comes out. Usually by then the extremely serious, gamebreaking bugs have been patched. That’s also early enough that the really good farming opportunities haven’t been nerfed yet.
Jubilee mob defeating achievement can still be done by doing the escort missions albeit much slower than with a zerg.
Invasion achievements counts regardless if the invasion succeed or not as long as you closed portals. Only the kill scarlet one would have a problem.