Do Battle Facility opponents count? Because if so, then I have two more Pokémon that I want to talk about.
The first one is Cradily. I have had some really annoying battles against it through the years.
The first one was against a Cradily in the Battle Tower in Diamond back in 2008. I was playing Double and trying to win 100 battles in a row at the Tower to get the final TC upgrade I was after, using a team of Bronzong/Starly/Dusknoir/Exeggutor. I had used successfully won 100 battles in a row on Pearl with this team, now I was using it on Diamond as well. I had lost once along the way, but I knew I could make it since I had done it on Pearl, so I made another try. I managed to make it far, and late in the streak (it was either battle #99 or #100, don't remember exactly which) I got into a battle where I only had my Dusknoir left against a Cradily. I don't remember exactly how I ended up in that situation, but I believe it was a combination of misplay from my side and good moves from my opponent. Either way, it became a long stall battle.
The Cradily had a moveset of Toxic/Double Team/Stockpile/Ingrain and it was holding a Leftovers, while my Dusknoir had a moveset of Night Shade/Will-O-Wisp/Protect/Rest and was also holding a Leftovers. The Cradily couldn't KO my Dusknoir with Toxic because I had Rest, but I could not hit it much either because of Double Team. It quickly got to +6 Evasion, I only managed to hit it with one Night Shade and burn it with Will-O-Wisp. Then, at the end of every turn, it would recover back the HP it had lost from the burn with Leftovers and Ingrain. It made the battle take forever, I'm glad I play with animations off so that it was at least somewhat bearable. The battle came down to struggling in the end, and I did not know that the Struggle mechanics had changed from Gen 3 before that battle, so I got super scared when I saw Dusknoir hit Cradily through +6 Evasion and lose 1/4 of its HP in the process. Dusknoir started to Struggle one turn before Cradily, but I still managed to win because I was at full HP while the Cradily was not. That battle was extremely painful, it took so long to complete to the point that all battles I had afterwards felt like they went by extremely fast in comparison. Back then, it was the worst stall battle I had ever had, and it was one of my earliest stall battles too. I still consider it one of my most memorable battles ever.
However, that was not the end. A few years later, in 2014, I was battling in the Battle Maison in X. There, I got into another stall battle against a Cradily! XY Battle Video: Q9HW-WWWW-WWW4-PEBB if anyone wants to see that. I don't think it was quite as bad as the battle in Diamond though, and I won this one as well. But then, a few battles later, I ended up losing that streak... against a Cradily!
There was also one time in the Platinum Battle Factory where I met another Toxicstalling Cradily and lost, even if I had a Magnezone on my team. However, I made a mistake in that battle as I used Thunder Wave to paralyze the Cradily, essentially giving it more turns since it could now become fully paralyzed when it got lucky, prolonging its life before it could start to struggle. That ended up costing me the battle.
Because of these battles, I always feel a bit of fear whenever I see a Cradily in any Battle Facility. I like to think of it as one of my unlucky opponents in Battle Facilities.
The second one is Escavalier. Not as bad as Cradily, but still annoying.
In the Battle Subway, I have experienced many losses and hard battles against Escavalier, especially Escavalier-4. The combination of Megahorn, Custap Berry, Swagger, good bulk and only one weakness (Fire, a type I usually did not have any offensive moves from) usually ended up giving me trouble. I could almost never OHKO Escavalier and it could usually KO me back or at least cause massive trouble in some way. I lost several battles where I was up against Escavalier, mostly in Double but two in Single as well. One of these was last year during my return to the Subway. It was against Escavalier-1 and it was in Battle #2, an early and very embarassing loss. There was also one time at the Battle Maison in X where I lost agaisnt a team featuring an Escavalier. It was when where my Super Rotation streak ended, I recall it involving a bit of misplay from my side too. Because of all these losses, I consider Escavalier to be another of my unlucky opponents in Battle Facilities.