as mentioned above with the ground sloping toward the pond if there is any exposed soils it could be an endless battle. Planting a thick stable vegetation on the way to the pond can easily resolve that in most cases.
Look at the bog as a separate pond and it has a stream leading from one pond to the other. and how ALL streams cut there way by erosion into the soil. so dig a trench . Start at the edge of the lower pond now you have to think is the flow of water going to be weak enough that gravel and some rocks laying on a rubber base will stay in place or will you need to dig a bit deeper and line the bottom of the stream with flat rocks that you can lock in place. with each other , some spray water fall foam , or even mortar. now so long as the rubber liner or hdpre runs into the pond you should not loose water.
Now the sides of that same trench you'll want create a shelf one that will be blow the water liner so that you can seal the water with foam and keep the flow of water ontop of the rocks and where you can see it and now run under them. the top of the same rocks needs to be higher than the edges so you can fold over the rubber liner and hidden by the rock and some gravel or soils on the other.
Run that rubber up to the bog or you can have the rubber all be one piece that runs into the bog i suggest the stream liner be run up into the bog and then the bogs liner run over that and don't be stingy with the rubber here you'll want it to be a wide area especially the higher the falls and the greater the flow rate.
Making the falls area in the shape of a flattened out horse shoe is best or you'll need a nice wide area for the water to fall into. The splash is a challenge to control . anyone who has seen a public fountain has probably noticed the water splash well outside the base of the fountain. that maybe ok for a public fountain . but when you have to replace hundreds of gallons a day or week it's a lot cheaper and easier to control as much as you can. The larger rocks to each side catch any splash that may occur and under both of the bolders and going well past is the same liner so if any water should get past these it finds it's way back into the pond.