Not sure what the best definition would be. I think it doesn't involve the DLC levels for sure since not everyone has it without spending extra I think. All levels w/ DLC could be separate if that's the case. I'm not sure about bonus levels though. Otherwise it would just be the 50 main levels.
I did one run of all levels NG+ once (just the main 50), but it was bad and I had intended to do it again so it never got highlighted. It was somewhere around 1:20 for reference.
I deleted my other posts because they're objectively wrong. If we want to do IL submissions it would have to be full video including the score screen afterwards. Leaderboards break after getting a perfect and then doing fastest possible times. Score could be use as a tiebreaker in some cases, but only on perfects unless you reset the file between attempts which is stupid. Fastest level completions would have to be beaten by a whole second to be improved in this case.
All perfects doesn't seem like it should be a separate category, since it's basically just the ideal for a 100% run. You would also find people being more conservative in an all perfects run on some levels where the gold times are very lenient.
I was thinking about this myself recently and I'm basically on the same page. I think a simpler definition is probably "all xp" - so from new file to 9840 xp (which is basically just having a full blinged-out medal on every level), including bonus levels and/or codex entries if we want to do that
As far as doing levels in order - I would say whatever order is fine, since they aren't done in order for any% anyway. Menuing back and forth on level select is faster than ignoring upgrades from later levels or replaying levels to get stuff you couldn't get the first time.
Either way, if you have an idea for a category, go ahead and give it a shot. If needed, we can tweak definitions and titles later to make it a better fit, since it's doubtful your first few runs will be super optimized anyway.