Can he sketch a move like psystrike, spacial rend, roar of time, judgement, shadow force, doom desire, sacred fire, areoblast, bolt strike, blue flare, ice burn, freeze shock, glaciate, or secret sword?
Yes, Smeargle can sketch most signature moves. All moves listed in your question can be Sketched. However, there are some moves, including signature moves, that Smeargle cannot Sketch, depending on the listed below:
In any generation: Blazing Torque Chatter Combat Torque Magical Torque Mirror Move Noxious Torque Revival Blessing Struggle Sketch Shadow moves Tera Starstorm Wicked Torque Z-Moves In Generation II: Transform Metronome Sleep Talk Mimic In Generation IX: Dark Void Hyperspace Fury
In any generation:
In Generation II:
In Generation IX:
Source
Do not give me any credit for writing this list! That belongs to Amethyst, who wrote the answer from the source! If you were going to upvote this, please upvote the BA to the sourced Pokébase post instead. Thank you!
Hold up. Smeargle can indeed sketch any move EXCEPT Chatter, chatots signature move. http://bulbapedia.bulbagarden.net/wiki/Chatter_(move)
