Doodloo is... honestly, it's not that good. But then again, it's what you'd expect from the game's Smeargle clone. It's arguably better than what it's based on, with slightly better offenses and HP. Having access to every move via Sketch, including moves that would otherwise be unusable, allows it to at least do a little bit.
The Doodloo used by Turner in the final fight is a clone which looks remarkably like Mosmero. It is no slouch however - in fact, it is such a broken Pokémon it deserves its own section on this page.
Doodloo is made intentionally broken to make players rage-quit the game, and it and the rest of Turner's Pokemon are fought at level 100. It has a nearly perfect stat distribution of Attack and Speed and, in tandem with its ability Pure Power and Dark/Ghost typing, it is insanely overpowered. For a comparison with other Pokemon with Huge Power/Pure Power, Medicham has the highest attack stat of any non Mega Pokemon with Huge Power at 60. Even taking Mega Pokemon into account, Mega Mawile has 105 base attack compared to Doodloo's base 184.
Minimum stats are calculated with 0 EVs, IVs of 0, and a hindering nature, if applicable.
Maximum stats are calculated with 252 EVs, IVs of 31, and a helpful nature, if applicable.
The moves Turner's Doodloo has are Rampage, High Jump Kick, Extreme Speed, and Will O' Wisp. Rampage is a clone of Outrage but is Dark-Type. This means that Rampage gets STAB and, coupled with Pure Power, is insanely strong.