execute crontab twice daily at 00h and 13:30

Try this-: 00 01,13 * * *

it will run at 1 A.M and 1 P.M

You can't do what you want in one entry, since the two minute definitions will apply for both hour definitions (as you've identified).

The solution is (unfortunately) use two cron entries. One for 00:00 and one for 13:30.

An alternative is perhaps to execute one script at 00:00. That script would execute your original script, then wait 13.5 hours and then execute that script again. It would be easy to do via a simple sleep command, but I think it's unintuitive, and I'm not sure how cron manages such long running processes (what happens if you edit the crontab - does it kill a spawned job etc.)

You can not do that with cron on a single line. You have to create 2 separate lines like so:

# Will run "YourCommand" at 00:00
0   0   *   *   *   YourCommand
# Will run "YourCommand" at 13:30
30  13  *   *   *   YourCommand

Or as a single line you can run a command every x hours, like so:

# Will run "YourCommand" every 12 hours
0   */12   *   *   *   YourCommand