(Note that this answer is primarily aimed at competitive play. If you're doing an in-game playthrough, consider teaching Dark Pulse, Shadow Claw or Shadow Ball to your Pokemon via TM to deal super effective damage to Musharna. Dark-type Pokemon are immune to Musharna's STAB and can carry moves like Crunch or Night Slash that can take it out quickly.)
By base power, Shadow Force and Megahorn are tied as the most powerful attacks to use against Musharna (120 base power), but due to the former having limited distribution and being a two-turn move and the latter being unreliable, they might not be the most consistent or available options. I'll go through some of the moves that I think can help the most against Musharna.
In my opinion, Knock Off is the most threatening move to Musharna. It will take super effective damage from the move, and it will have its held item removed. Musharna typically runs Leftovers, so removing that spontaneous turn-by-turn recovery can help significantly in taking it out. Knock Off is also a great move in general, as there are very few switch-in Pokemon that don't mind losing their item permanently. Knock Off lacks its initial firepower on any consecutive use, however, so you may choose a more consistent option such as Crunch or Dark Pulse to deal with Musharna. You certainly should not overlook how helpful Knock Off is, though. Hyperspace Fury is also a good move as it breaks through Protect, but it is only available on select Pokemon.
Some other good options you can use to threaten Musharna or use to gain an advantage include Pursuit and U-turn. Pursuit is great for any Dark-type Pokemon that may tempt Musharna to switch out, as it will deal double damage if it does choose to do so. If you catch Musharna low on HP, Pursuit can be great to trap it and ensure a KO. U-turn is a great way to gain momentum by predicting Musharna's moves and switching into an appropriate Pokemon. A slow U-turn can allow you to let a Pokemon switch in without it taking a hit. Musharna is weak to the move, which makes it an especially good option.
Super effective moves in general can be the biggest threat to Musharna, especially if they can score a 2HKO and thus cause Musharna to lose 1v1, as Moonlight cannot allow it to profit in HP. Shadow Claw, Shadow Ball, X-Scissor, U-turn, Dark Pulse and Crunch are some good options with a wide distribution that you can use to threaten Musharna. Be sure not to exclude status moves from the equation, either; Musharna is crippled by moves like Taunt that prevent it from using Moonlight and Calm Mind, its most valuable assets in competitive play. Musharna despises status moves, especially Toxic which essentially puts it on a timer. Be careful when you do this, though, as Musharna has the ability Synchronise. Trick and Switcheroo permanently shut down Musharna if you can get a Choice item onto it. Musharna also dislikes entry hazards that prevent it from switching in too easily; Toxic Spikes can be helpful to poison Musharna risk-free. Dark type Pokemon pack an invaluable immunity to Stored Power and Psyshock, Musharna's best offensive moves, which makes them good options to fight Musharna, on top of their access to STAB Knock Off and Pursuit.
If you're in an in-game play-through, it's best to target Musharna's weaker Defence stat, but in competitive play, most sets use full Defence investment, so special attacks do the most damage. This does not mean you should overlook physical moves as a means to threaten Musharna, however, especially since Musharna can boost its Special Defence with Calm Mind and thus make it harder to hit with special moves.
