Understanding glyph origin of 勤 better I have the following etymology from Outlier Dictionary of Chinese Characters:
勤 qín is composed of 堇 jǐn “a type of ancient punishment in which fire was used to dry a person out” and 力 “force, power, effort,” pointing to the original meaning “toil, labor.”
my question is this punishment  killing the person with fire? or make him sit near fire to dry up? Please explain high level this punishment to understand the character better. thanks
勤 is phonetic 堇 + strength/power 力.
堇 has few interpretations. One is clay (yellow soil 黃 + 土).
Another is possibly a person being burned alive as a punishment  + fire 火. The character with this punishment meaning is 暵 and is not really seen in modern usage.
 is the basis for these 2 characters 難 and 嘆, meaning difficult and sigh respectively. It's a person with inflamed lungs/chest breathing in pain.
Unlikely there's any link from 堇 to 勤 with regards to its meaning, so if you want a sort of mnemonic, think of 勤 as hard work requiring strength 力 to overcome difficulty /難.