The JIRA Import Wizard worked for me. Maybe they've fixed a bug in the last year.
JIRA home screen > Settings > System > External System Import > Trello
It will import the Trello cards into a new Project (wouldn't let me pick an existing project). You can then Move the cards into your actual project; the Move will let you map the newly created statuses (from Trello) to existing statuses in your actual project. The last screen before you confirm the move will also let you see what fields it's going to drop.
Can you export projects from Trello to EXcel or XML file? If so you can import project to JIRA using e.g. CSV file
A Trello Power-Up called "Jira" allows converting and linking individual cards to Jira boards. Look for it in the Trello Power-Ups store.
Additional info is in this Trello news post: https://blog.trello.com/trello-power-ups-for-jira-bitbucket-confluence-hipchat?utm_source=powerups&utm_medium=meta
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