You weren’t far off
> The writer J. R. R. Tolkien coined the word by affixing the Greek prefix eu, meaning good, to catastrophe
From the New Oxford Dictionary
> Catastrophe: mid 16th century (in the sense 'denouement'): from Latin catastropha, from Greek katastrophé 'overturning, sudden turn', from kata- 'down' + strophe 'turning' (from 'down strephein 'to turn').
It looked funny pairing for bit of Greek I know until I read the link and realized it wasn’t really Greek.