Just some initial thoughts, though others will come soon with much better ones I'm sure. Try and see what defensive branch the drengin are going after, and change your weapon research to counter it. Also, research shields and such to try and decrease the effects of their beam weapons. In my previous games, the AI will "usually" follow one weapon type for both offensive and defensive. For instance, most times if I see their ships are using beam weapons, I'll notice they've also researched and added shields. So by researching a different offensive route, you can make a bit more of a dent than say if you followed suit and also went after the beam weapons.

Naturally though, if you're already far along in say your beam weapon research, it might not be in your best interest to change your focus. Anyways, just thought this might make some sense and try and offer a bit of help.

It's possible there's some game mechanic you aren't exploiting. Like, are you banding your ships together in fleets? A fleet of several weak ships can often take out a strong one. Are you designing your own ships?

If you've played the first GalCiv you know that this is not the kind of game where you can rescue yourself from ship inferiority with tactics. You have to build an economy that can compete in technology and ships, so a lot of the time the answer to "how can I compete" is "by playing better 200 turns ago." Maybe you needed to develop a survey ship by researching Sensors so you could find money in the anomalies. Maybe you needed to settle fewer planets so you could develop them without going broke. Et cetera.

The Drengin spend so much on ships, they lag behind a reasonable power in terms of tech after a fairly short period of time. So if the Drengin are beating you at anything other than the earliest era of the game, you are probably doing something wrong.

You really need a fast expansion in the beginning. It will increase your population and therefore your tax revenue. You need to set your research relatively high so that you have the technology. You also need to understand why you are being attacked: your navy is weak and the Drengin see you as a quick invasion target. Good luck.

I've just started playing GalCiv II, and even though I never played 1, I did play Ascendency, so there's a lot the same. For that mission (which I'm part way through at the moment), I just colonised all the planets before they could, and I'm going for a simple defense with one mil base and four ships while the planets build up until I research planetary invasion, then I'll take theirs and win it. As you can see by this strategy, apart from some simple tactical decisions about where to put the mil base and where the two ship-pairs will be it's basically just an economic game (keep capacity up to 100 for most of the game) which I personally find easy. If you do this you'll win way before you get large ships or any weapons more advanced than laser 2 or 3, but it all depends on how you can manage your economy.

They could have a mil base of their own, which would cause some trouble if you try and fight them when within range. Instead, find the mil base, see how well defended it is. If it has no defense, just get one or two little ships that are pretty useless to make a dash for the base and destroy it. If not, get to it with a good fleet by out manouvering the enemy while they are in the mil bases range. Also, this map has plenty of resources, in my opinion, don't bother capturing them, by the time they produce a good enough effect to counteract the cost of your contructors the game will be over.

Stacking your ships is not the same as fleeting them together. To form a fleet, select all the ships you want to be a part of the fleet from within the stack, and click the "Create Fleet" button. There will then be a single icon for the fleet of ships, and if you zoom in you will see two or three ships occupying the square together. You will have to have a logistics rating as high or higher as the combined logistics size of the ships you are trying to combine into the fleet. You can see both in a ###/### format at the upper right corner of that window, near the "Create Fleet" button. 79/123 would indicate 79 logistics points used out of 123 logistics points available.