How to impress superiors without being a brown noser?

Ignore them. Brown noser is what lazy people call achievers...

My advice is FIDO "something It, Drive On!"

I agree with SFC Jolly and SSG Hasbun. Give your job everything you have, do the best job you can, prepare yourself for the next job. Let your leaders know that you have drive. Volunteer when it makes sense (and you can without burnout).

Remember the people who displayed a lack of drive on your way up. In 5-6 years, you will be having to counsel them on their performance. ;-)

Sounds like you're doing everything right and receiving attention already. If your coworkers are noticing, your superiors are noticing as well. Don't let the lazy ones drag you down to their level; keep up the good work!

First things first...learn the difference between colleagues and peers. Colleagues work on the same type of task(s) as you do. Peers work at the same level as you do. It matters not what colleagues say and think unless you can genuinely call them peers. Just ask yourself...when was the last time you saw or heard of a hater hating on someone that wasn't successful? As long as you're not rolling over someone else to achieve your goals let those haters hate. They have to earn a paycheck some how. Just let all that "hater-ade" keep you hydrated as you do your thing!

One other thing...don't settle for only impressing your superiors, but also ensure you continue to impress yourself. You find out, if you haven't already, that sometimes you will be your biggest supporter and fan.

A lot of people will present this as brown nosing, but a lot of people are lazy. The best thing you can do is the job you are assigned to the best of your ability. The ones that spend the extra time doing the job right are often pulled out to do more work, and when it comes to promotion you'll be selected only half as many times as what you expect. You should always want to do the best you can, as there is a greater cause of more then you can see.
So never let those people hold you back, and after a while those individuals will leave you alone in the work environment. Eventually they will part ways with the military or clog up the system. You mission is to find a way to see your ways and follow them, as a good leader would.

Continue to do your job to the best of your ability. One of the biggest kickers is to ensure that you do not point out to your superiors what you were doing, because then it just looks like you were saying look at me look at me. In my opinion that is what a brown noser is.

Working hard is not brown-nosing.

This is brown-nosing:
"What kind of sycophant [brown-noser]are you." -Cruella DeVil
"What kind of sycophant would you like me to be?" -Assistant

Work hard, be genuine, be yourself... Don't let the opinions of others make you change what you do, especially because they call you a brown noser... It's probably because you posses the qualities that they wish they had.

I think a lot of the answers have already been provided here. I think you've got some ambition going there - that's a good thing. Keeping your perspective is also important. Wanting to impress your superiors just to impress - sorta short sighted. Have a goal. You may already have one - but you didn't state it in your quest for answers. You should actually have at least 3 seperate goals professionally - short term, middle term and long term. The short term one is uaually the one the Navy puts in front of you - either a technical proficiency or a promotion. Take the technical proficiency first, because it will take the greatest time and have the greatest affect on your promotion, especially at your current paygrade. For the promotion - knock out all the online training required long before the deadlines. I don't know if it's still possible, but I had completed all the mandatory online/paperwork training for my potential promotions all the way to Master Chief before I made my first promotion to E-2.

For your middle term projects - plan for things like ESWS or your dolphins as soon as possible. When you get onboard you will find yourself with a huge amount of work to do regarding learning the job functions as well as learning the ship/submarine functions - don't sweat it. Put in the time and effort to learn the systems - ALL of them. On a submarine, there is no one more useless than someone that doesn't have their dolphins, except for someone who isn't working on their dolphins 24/7/365. You want the respect of your supervisors/superiors - EARN THAT PIN.

Long term....decide early on whether you want to go warrant, LDO or stay in the enlisted ranks. Never say never to an opportunity - but take the time to realize the risks of failure and rewards of success. No matter which you opt for, understand that life does not always agree with your plans or timing. Be willing to sidestep if necessary.

Finally, make a plan for financial success. If you're not saving at least 70% (or more) of your pay as a single sailor and at least 30% of your pay as a married sailor - you're doing it wrong. I was told that if you didn't save at least $50,000 in your first 4 years (without bonuses, just regular pay) then you were doing it all wrong. For a sailor only making about $300 a payday that seemed unattainable - but I did it.

Treat the Navy like a civilian job in the sense you need to come to work to work. Let the quality of your work speak for itself, seek a quality mentor and utilize them. Don't be afraid to take on new responsibilities. Document your man hours of maintenance, qualifications and achievements to assist in providing actual analytical data for your eval. If you act like you don't care about the direction of your career no one else will, and last but not least never let on your intention is to separate especially around eval time.