Board Thread:Questions and Answers/@comment-25009284-20141129235813/@comment-3241231-20150323034126

1) It might be worth it, but for most party health monsters, it's simply 1 million. It's definitely worth noting for the exceptions (Leviathans, event Cronuses) though.

2) Again, generally the same for most monsters - 200k. The exceptions in this case are the earlier (chronologically) monsters; (Alpha) Bahamut and Azriel have something like 670k for their bars, before the devs realized that it was basically too difficult.

Looking back, that note on strengthening is basically flavor text - there's really nothing particular that happens at those thresholds or anything.