Level-based Accomplishments.
These days achievement-based rewards are considered awesome. You want more than just the grind and grind and grind to get itemX.
Specifically I'm contemplating along the lines of:
Finishing a level:
a) Without taking any damage.
b) Using only a single weapon.
c) Not picking up a single drop.
d) Using only vials.
e) Not killing any monsters. (clearly wouldn't work with all levels)
And there being a level-based reward.
Complete a Wolver den only using a single weapon? Not a big deal.
Complete a Haunted Passage with a single weapon? More difficult.
Complete an Arena with a single weapon? Quite a lot more difficult.
* Defeat Lord Vanaduke with a single weapon? Yay, a 4-star item for you.
* Defeat Lord Vanaduke with incomplete equipment? Congratulations on a 5-star material.
* Defeat Lord Vanaduke without taking any damage? Congratulations on a specific, pretty awesome 5-star piece of equipment.
Etc.
Knowing that such things require tracking, contemplation of implementation is best done early. This would also give people something to chat about.
Purely optional, on top of everything else bonuses. You can still do whatever level however you want. You just get something extra for doing it in some exceptional way.
I hate achivements, I feel they add NOTHING to a game more than a meaningless arbitrary task. That they are a excuse so devs can add content without actually doing anything meaningful.
So, I'm against this.
Sounds good to me. I'd bet achievements/trophies will be added at some point, since other OOO games have them. Unique objectives would add some nice variation.
Alternatively, levels could be built from the ground up to require a unique play style. A level could be designed to only let you use swords (and it would have to give you a temp one if you don't have one equipped). There could be a level with all invincible enemies.
So yea, all for great variation in levels that are built to make you play in an unusual way. And all for something that will encourage you to play the existing levels in an unusual way.
In terms of rewards for doing these, I'd say really weak but uniquely designed helms or somethings would be cool. A helm that looked like a trophy or something would be fun.
Regardless of my personal opinion on them, achievements are a shrewd move commerically.

Regardless of my personal opinion on them, achievements are a shrewd move commerically.
The fact is that many people enjoy have smaller goals that they can work for. It adds variety and encourages people to get out and play. I personally have been motivated to play because of some random achievement in various games. Assuming that it's not the only way to get X useful item that gives an actual game-play advantage, I'd enjoy seeing something like this here.
I don't think all of you understand what this suggestion actually entails.
He didn't suggest achievements/trophies. He's suggesting secondary objectives for increased rewards, like beating a stage with no healing items or within a time limit. This allows the player to increase the difficulty level of stages in specific ways. The rewards would be improved, but not exclusive.
And for the record, every single one of Three Rings' games (including Whirled) has features achievements. Don't expect Spiral Knights to be the exception.
Having floor specific objectives (probably a better word than achievements) that grant bonuses would add a lot to the game. I think the rewards should be greatly toned down from what you suggested, but the concept is very solid. Some really creative things could be done, such as a speed run per floor that give extras if you meet the speed requirement. That could even be expanded to include a Haven to Core speed run that would track the speeds of all participants and award the fastest X players with prizes every week they remained the fastest.
I wasn't thinking rewards along the lines of the ones I listed for something that might apply to normal floors. It'd certainly feel excessive to get a R4 or R5 item per floor.
And yes, some term that doesn't come with the baggage of 'achievement' would be excellent.
I think a large part of the potential is that scaling such a feature requires a smaller degree of developer time, yet still adds a lot of variance and 'stuff' to do.
I think I've suggested somewhere before that trophies would be a good thing to flesh out our currently bare guild halls. Guild members could see the achievements of others, both in their guild and globally, and compete to beat their scores.

The guild hall has a really conspicuous pedestal for a statue, trophy, or whatnot... it wouldn't at all surprise me to hear that more guild updates are being planned. :)
I still think that Guild Halls should get a gate (or two) of their own. It seems futile to try and publicly organize a gate's donations... but in a guild it becomes far more likely, and fun!
That just sounds painful.
And by painful I mean, if I had a samurai sword I would be using it to turn my guts into sushi and still be having MORE FUN than I would playing SK.