Hello there.
I can see that the plugin you linked is supposed to be compatible with Yanfly's Battle Engine plugin, but I am unsure just how far that compatibility goes. I don't have a leTBS project set up to test from at the present, and it will not be a quick task for me to do so, as I don't personally use that plugin myself.
Since I'm not sure how much of BattleEngineCore actually makes it into use in leTBS, I'm not real sure where the incompatibility actually is. It could be as simple as the Attack Times+ trait not functioning in leTBS, or it could be as complex as action sequences not being implemented at all. Or both.
To start, could you describe what does or doesn't happen when testing in your own project? Does a second attack occur for dual wielding actors at all, just with the wrong damage/animation/weapon, or does only one attack happen? If only one attack happens, does it show both the battle animations for each weapon on top of each other, or just one animation? Does it simply crash and not work at all?
I expect the menu stuff should probably still be working fine, except unless leTBS has some sort of in battle status menu, in which case it would need to be patched to work with the offhand weapon slot properly.
I can't guarantee I'll be able to patch it to make it compatible, but I can give it a shot.
-Ramza