For the new folks, The Decisive Battle of Nidhogg is a campaign with two parts, each differing in mechanics. A Nidhogg iteration typically doesn't associate itself with the event it "piggybacks" on.
The first part, Twilight Underlings [link], involves fighting Nidhogg minions, while the second part, Sweltering Heat Maze [link], features the inside of Nidhogg and has sets of tiered stages, up to the Core level. Flower Medals, the Nidhogg-only currency, can be earned from these stages. The links have the mechanics on each part. They're quite extensive enough that I won't have to type everything here. Feel free to ask if you want clarifications though.
"Strongest" in this sense pertains to Underlings on the last wave (Wave 3/3), but in terms of day-by-day increase in difficulty? Subjectively speaking, no. In the last Nidhogg iteration (November 2018), I was able to win* with only "1 Turn" (on the turn counter) in majority of the fights, except on days where I struggled with trying to match the attribute(s). The only other, and more notable, change that happens daily (at 00:00 JST) aside from their appearance is change of weaknesses.
*Win condition in Underling battles is defeating all 3 waves in 5 turns or less.
Milestones are just there simply as milestones.
It was on the 4th Anniversary Nico Livestream's table of plans after January. Also, it's been over 2 months since the last one, so we were due for this anyway.