Arch-enemy seems in a bad way (7)

I believe the answer is:

nemesis

I'm a little stuck... Click here to teach me more about this clue!

'arch-enemy' is the definition.
I can't tell whether this defines the answer.

'seems in a bad way' is the wordplay.
'a bad way' indicates an anagram (I've seen this in other clues).
'seems'+'in'='seemsin'
'seemsin' anagrammed gives 'NEMESIS'.

Can you help me to learn more?

(Other definitions for nemesis that I've seen before include "Vengeful justice" , "Avenging deity" , "E'en miss (anag.)" , "Greek goddess - opponent who cannot be beaten" , "Goddess of retribution in Greek mythology" .)

I've seen this clue in The Daily Express.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.