With MilkyTracker (
http://milkytracker.org/), a standard module tracker. You can sequence your music with this, especially if you connect your MIDI controller so it's easier to record.
This guy here is famous for his module tracks made in under 60 minutes (from an internet competition):
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http://coda.s3m.us-
http://coda.s3m.us/about/He uses OpenMPT (
http://openmpt.org/), which you could also give a try.
Then you can finalise your module tracks by rendering them to PCM (wav or mp3) and importing to LMMS (
https://lmms.io/showcase/) as "Sample Tracks". Here you can use automation and further editing.
You can also sweeten \ edit sound effects with LMMS, but this would take more time than just using those chiptune sound-effect generators that are common in these speed competitions.