I collected the “finish with 5 deaths or less in gravity” quest and so far I’ve had a game with 0 deaths, a game with 1 death, and a game with 2 deaths none of which have counted for this quest.
Hey there 
Thank you for taking the time to report this issue. It has been logged and you can look forward to a fix in a future update.
Stay safe and well
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Hey there
This issue has been fixed 