There is no adapting difficulty according to player stats. However, there are cases where the difficulty does increase without player input. Each time you advance a loop, the difficulty will increase by 1. Each time the depth increases in the chaos dungeon, the difficulty increases. There is an event in dlc 3 that sets the difficulty to 9 (the max, outside the chaos dungeon anyway). You can set the difficulty yourself at the statue in the library on the top right(and also see how many times you've died).
Some enemies have attacks that deal damage based on a percentage of your health however. In the main game, that is outside chaos dungeon and dlc 3 area, I can only think of the god fish's slam attack, very notable since it does 100% pretty sure. Dlc 3 has a bunch though, even regular enemies have them sometimes.