Can you stun the attacking unit when they are defending during a Showdown?

Yes, you can stun a unit that has the "Attacker" designation even if it is currently participating in a showdown.

According to Rule 410.1, stunning is the act of selecting one or more units on the board and rendering them stunned. There is no rule that prevents a unit with the "Attacker" designation from being targeted by a stun effect.

However, keep in mind the following:

• Stun is a Limited Action: Per Rule 410.2, you can only stun units when directed to by a game effect (such as a spell or ability).
• Combat Impact: Per Rule 410.1.b, a stunned unit does not contribute its might to damage in combat. If you stun an attacking unit during a showdown, it will not deal combat damage when the showdown proceeds to the damage step.
• Designations: A unit's designation (Attacker or Defender) is determined by the player who controls it and the battlefield it is on (Rule 442.1.a). Stunning a unit does not remove its Attacker or Defender designation.