Your health drops by 5HP every 5 seconds or so till it reaches 25HP, putting you on a very tight leash in terms of HP. You receive the soul cube in level 2 when playing on nightmare, this allow for some new strategies which actually make some parts faster on nightmare, for example the first mini boss Vagary can be killed in around 5 seconds compared to around 20 seconds on marine.
All medkits are removed, only way to restore health is to use health stations or the soul cube. Many shortcuts that involve taking damage can't be used, the damage system for nightmare makes everything deal a ton of damage and often result in instant death.
First of all, some things that I can't do are rocket/grenade/barrel jumping, a single explosion bring you down to negative health (instant death) when you have full health and armour. There are of course a bunch of differences between a marine run and a nightmare run in style of playing and strategies as well as the choice of shortcuts and time savers.
When Jérôme "tagh_azog" Bouzillard got his 1:30 run on marine up the goal became to beat that run, with the difference that I would be running on nightmare instead of marine. This is probably one of the hardest things you can do in any FPS game. The planning started back in August 2005 and I guess that the time it took to finish this is a good measurement for how hard it is to speedrun this game on nightmare. This is a project that has been going on for several months and I even restarted the run from scratch twice because I wasn't satisfied with the result. Appended into one file and available in 320x240 and 640x480 versions.
Speed run of Doom 3 on Nightmare skill in 38 segments completed on July 14 2006.