Black Knight 2 is very tough for the point he appears at, and you'll need every advantage you can get against him. His Barrier Shift is random, with an equal chance for each element. Packing at least a few potions of each type is a good plan, so you can take advantage of a given weakness if you get the chance.
You can build up status effects even if BK isn't weak to them at the moment, and they'll take effect when they can; if he switches to Ice weakness while he has a 40% Chill, for instance, he'll suddenly have to deal with the effective 60% slowdown from that, and some extra Cold Snap damage if you've hit him with that too. The caveat being, whether he switches to it at all is random, so you'll need a little luck.
He'll also use Twister more often when he's Burned or Softened even if he isn't weak to those elements at the moment.
Rock Wall stacking is a powerful strategy in general; Super Powder of Rock + Molten Iron will give you +18 Defense before any other modifiers, and if you have Stone's Throw, that translates to a solid attack boost too. Just be sure to pack extras as Black Knight can cast Torrent II to chip away at a Rock Wall.
Erosive Phials will break down a Rock Wall even if Black Knight is currently immune to their damage, and have 15%/15% timing to Shaker II's 20%/30%. It'll take two to break the 4-turn wall that Shaker II creates, but timing just one so that it comes out while Black Knight spends a turn on Iron Ball would leave him wide open.
Another option is Catalyst formulas, as the Trigger deals Neutral damage, Catalysts can be stacked whether the foe's Blocking or not, and Catalyzer Focus has no issues since the Black Knight has no Gravity attacks. If you've got a bunch of Jelly Jewels, you can potentially blast him down in one explosion, or get him close enough for a Grav Formula to finish the job.
Finally, there's one available sidequest in particular with a reward that's both generally useful and very strong against the Black Knight's signature Block/Iron Ball combo.
EDIT: Wait, tabbing out can stop the graphics from updating? I've never experienced this issue, where did this happen?