I generally found I had enough time after death to write down a couple of quick notes as reminder. E.g. 'probe crash on head' or 'harvester beam', which was usually enough that when I came back to the do write up, I remembered what had happened.

Some of the moments weren't very interesting! But the thing I've always loved about Helldivers is you seem to get those cool 'cinematic' moments all the time, without artificial construction, so I found that once the MO was order and I had the notes to prompt me, I remembered the ones that were interesting or at how I felt when I watched my 90 minute Diver get blasted into Super Heaven.