Understanding glyph origin of 勤 better
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.