How do you deal with NCOs that severely compromise the corps Values?

I agree that pull him aside and be professional. However, I would have another soldier equal or higher in rank with me to cover my six. If that does not work, bring the issue up the chain of command. They might know already, but waiting for the soldiers to say something.

You make them E-3s

Senior leadership, if doing their job need to catch and address this. However, I learned as much from toxic leaders as I did good leaders. Pay attention to what troops respond to

Suck it up, and press on. Life is not fair, but you can handle how you react and deal with it. Do your best. If an NCO treats subordinates in that way, it does not go unnoticed to his superiors.

Luckily I never had such a situation. I never had a company commander or a 1st SGT that would have allowed it. Probably I was lucky.

take it higher up

SFC (Join to see) use your judgment be assertive in your communication approach the SSG and be firm in your convictions. If a one on one conversation does not resolve the problem. Inform your supervisor.

SFC (Join to see)
Eventually we all answer to someone BUT first, as a leader, I think the first step is to go to this leader and find out why they are acting the way they are? Sometimes, when we are brought into all the information, our opinions are changed, sometime they are confirmed and sometimes we are able that the truth is somewhere in between?
If there is something needs correction, point out what you consider the error and offer a possible correction? Often, we assume someone knows something...especially those of higher rank...when they are really not aware of their errors? "We have always done it this way?" "That is how it was done to me?" ETC.

I will blame the Officers in charge for not being vigilant and for failing to not have a good open chain of command that counters the effects of poor NCO's.

Try and speak with this NCO and if that doesn't work your unit should have an open door policy in place, just remember there is a chain of command you should still follow but if you think it will go nowhere then go to the 1stSGT and Commander.