I found some more info about the Anglo-Russian invasion of 1799:
At 12-8-1799 a fleet of 176 ships departed from Yarmouth and took 15.000 soldiers aboard in different harbours. The supreme commander of this army was the Duke of York.
At 15-8 the allied army occupied the island Schiermonnikoog and prepared a landing at Den Helder on the 22th of august. The landing had to be prosponed due to changing wheather conditions. Eventually the army landed five days later at Callantsoog.
The first soldiers who landed, were 2500 veterans, commanded by lieutenant-general Pulteney. After three hours, about 7000 men were positioned on the beaches. Lieutenant-general Abercromby took over Pulteney's command and advanced to the south.
The advance continued and the city of Amsterdam was threatened by the allied army. At 19-8 a combined French/Batavian army achieved its first victory.
After Russian troops, commanded by general Hermann (nice Russian name

... might be a Prussian officer), occupied the town of Bergen in the morning, the French supreme commander Brune reconquered the town. General Hermann was captured. 3986 English/Russian soldiers were killed that day and 3710 soldiers of the French/Batavian army.
So this must be the battle of Bergen, one of the three battles i mentioned in my previous post. As i can't find any info about the other ones, i don't know if this has been the decisive battle.
It's for sure however that the Batavian Republic remained to exist because of the failure of this invasion. Until Napoleon installed his brother Louis and the republic changed into the Kindom of Holland. In 1810 the Netherlands were annexed by France.