Was thinking what attacks Bintunia would know, that would make sense from a trainer's point.
Since Smeargle's have crappy stats I went for attacks that work independently of stats (mostly). All of her training went into raising her hit points so she can survive as long as possible to whittle an enemy down. She'd probably carry something to heal her back up.

SUPER FANG: Halves an enemies' health, regardless of defenses or health. Great to cut down the HP monsters and rock/steel defense pokemon.
Bintiunia learned it from a Rattata, thus she grows incisors during the attack.

TOXIN: Kills surprisingly quick. Great against (regenerating) HP monsters.
Learned from a Smogmog. It turned her tail paint permanently purple and toxic (she is immune to her own poison). She uses it by painting a skull onto her opponents.

ICE BEAM: The exception from the rule. Ice attacks are one of the less common elemental attacks and one of the few able to double damage dragons. There are also no immunities against it and few resistant elements making it a nice finisher once Super Fang and Toxin have brought the HP down. And if the freezing effect activates its pretty much a sure win.
Bintunia learned icebeam from a Delibird.

4th attack?: Not sure yet. I was thinking about either Teether Dance (Since Smeargles can have Own Tempo which makes them immune to confusion) or something that buffs both Special and Normal Defense to again increase her survivability.