Thanks for the reply. I could drill into the bedrock. The problem is that it is on a rather steep slope, where at the shallow end it is only about 50 cm (20 inches) deep and at the deepest end it is almost 200 cm (80 inches). The bedrock is a great seal, it doesn't leak any water from there. The problem is the sides that consist of very porous soil. This is one of the reasons why I would prefer not to use a pond liner, it simply wouldn't be necessary for the bottom of the pond. I want to find a method to seal the sides without covering the bedrock.
I have seen some videos where they use shotcrete. I don't know much about it, but it looks like it could be a possible solution.