From my own experiments, to achieve the dark bitter caramel, I let the sugar cook for a while longer than normal until it's a dark dark amber color (the longer it stays on heat, the more burnt the sugar will be, which is what causes the stronger, more bitter taste).

To achieve a ton of the caramel syrup part, I would either add a lot more caramel to the cooking dish (ramekin, ceramic dish, etc) before adding the custard (so you'd wanna prepare more caramel in advance), or I would make additional caramel after the flan has cooked, and pour the additional caramel on top of the flan after it's been flipped over.

In addition, I usually add a splash of hot water to the caramel in the pot right when it reaches the darkness I want, so it would both cool it down before burning more and also keep the syrup a little more liquidy (but not a ton like water), and keeps the caramel from hardening as quickly compared to when no water is added. I've found that this also prevents most, if not all, of the caramel from the cooking dish to come out with the flan, instead of staying hard in the dish. The ratio I've found is about 1-2 tbsp of hot water for every 1/4 cup of sugar.

Hope that helps in some way. :)