Difficulty

Difficulty is tracked by an internal number (from now on simply called 'level') that scales from 0-3 during the course of the game based on various factors. Entering "hardmode" adds 3 to the level effectively making it scale from 3-6. The stats of all Guardians, most Room Guards and a few enemies scale linearly based on level, using the formula, rounded to nearest whole number.

is the current level

is the lowest possible value of that stat they can have

is the highest possible value of that stat they can have, reached at 'HardestLevel' (which might or might not be possible to reach)

is the level where the stats are at its base value. It's probably always 0.

is the level where the stats are the highest. It's probably always 6 (or 9 for regular enemies).

The stats listed for a Guardian on their respective page is 'base-highest possible' (or a single number if it does not scale with level). Highest possible can only be reached in 'hard mode' due to the increased level, so for most players the actual highest stat is base plus half the difference between base and highest. As an example, Echidna's health is 256-320, which means her highest health in normal mode is

Hardmode
'Hardmode' or 'hard mode' is most often used to refer to the gamestate after reading a certain tablet in Mausoleum of the Giants twice, which increases the game's level by 3.

Hardmode is also the breakpoint in level where Guardians gain additional or alternate patterns, which is (so far in my research) always 3, meaning that even in "normal mode" the player will reach hardmode boss patterns by the end, and also that bosses will always have their new patterns if you opt-in to 'hard mode'.

If you activate 'hard mode' there is an opportunity to lower the game's level again by talking to Voluspa in Annwfn. She does however not lower it to normal levels, instead only lowering it by 2.

-TODO: Research how the gradually increased spawning of enemies work