How do you demote an NCO who is proficient in their work but your PLT SGT says that you're inefficient and has no evidence on how?

The Promotion Authority can reduce for inefficiency IAW AR 600-8-19 Chapter 10.
Excerpt below:
Section III
Reduction for Inefficiency
10–5. Policy
Inefficiency is a demonstration of characteristics that shows that the person cannot perform duties and responsibilities commensurate of the Soldier’s current rank and MOS. For the purpose of administrative reduction, inefficiency must be predicated on a pattern of acts, conduct or negligence that clearly shows the Soldier lacks the abilities and qualities normally required and expected of the Soldier’s rank and experience. Although CDRs may consider misconduct, including conviction by civil court, as bearing on inefficiency, misconduct alone will not be the basis for an administrative reduction under this paragraph. Soldiers may be administratively reduced under this authority for longstanding unpaid personal debts that he or she has not made a reasonable attempt to pay. An administrative reduction for inefficiency is limited to SGT and above and to one grade (unless formally declined by the affected Soldier, reduction boards are required as provided for in para 10–1c).
10–6. Criteria
a. A Soldier must have served in the same unit for at least 90 days prior to being reduced for inefficiency.
b. The CDR initiating the reduction action will present documents showing the Soldier’s inefficiency to the reduction authority. This may include:
(1) Statements of counseling and documented attempts at rehabilitation by chain of command or supervisors.
(2) Record of performance, acts, conduct, or negligence during the period concerned.
(3) Correspondence from creditors, attempting to collect a debt from the Soldier.
(4) Adverse correspondence from civil authorities.
c. Documents will establish a pattern of inefficiency rather than identify a specific incident.
d. Reduction for inefficiency will not be used for the following:
(1) To reduce Soldiers for actions for which they have been acquitted because of court-martial proceedings or civil proceedings.
(2) In lieu of UCMJ, Article 15.
(3) To reduce a Soldier for a single act of misconduct.
e. The CDR reducing the Soldier will inform him or her, in writing, of the action contemplated and the reasons. The Soldier will acknowledge receipt of the memorandum by endorsement and may submit any pertinent matter in rebuttal. Any matter submitted by the Soldier must be considered by the reduction board and reduction authority prior to rendering a decision.

However, in the USAR the Promotion Authority is not the final word, as orders are issued by the governing RRC. Brigade and above commanders would have to endorse the reduction.

You cannot demote a person in rank unless it is a disciplinary issue. And I do not believe that a commander can exercise UCMJ authority over a Soldier unless they are on active duty orders. Now they can reassign duties which could be looked at as a demotion in position. Even still, that should not happen unless there is a counseling record. Unfortunately in my experience, counseling in the USAR often leaves something to be desired. The Soldier always has the IG channel if the chain of command does not work.

Can't. In fact, one of the biggest disciplinary issues that leaders face is a "lack of evidence" when issues are presented. If you do not have documentation, as the saying goes, "it did not happen". You cannot approach a Commander and say "well there was this one time, sometime last year where x happened".
As a leader, you have to memorialize the good actions, and sadly the bad. The only way to demonstrate a pattern of behavior is to have documentation of it.
COL Jon Thompson Sir, there are now states that have implemented "State Codes of Military Justice" that mirror the UCMJ, but make it applicable to Guard units. So status stops being an issue for dealing with disciplinary issues.