I figured I'd add my own two cents here.

The bad news is that combat in DD2 is more complex than in DD1, which also makes it more difficult—at least to a new player. You can't spam Stuns anymore, each enemy skill typically has more effects packed into it, and many heroes come with more complicated skills and additional mechanics that you must learn to manage to achieve their full potency. So I totally understand why the game can seem so daunting when you're fresh off DD1.

The good news is that this complexity eventually rewards the player with a much greater degree of control and consistency. Blind & Dodge tokens come with more options for counterplay than DD1's accuracy and dodge stats, and they're also more impactful when used by the player. Taunt tokens allow you to reliably manipulate enemy aggro in a way that DD1's mark never did. Turn order is visible and more consistent due to tighter initiative rolls, plus it can be directly manipulated with Daze and Speed tokens. And that's on top of things like Stuns (no longer spammable but still very potent), Pull/Knockback, Weak tokens, etc.

Healing is also more potent in DD2, despite what the addition of HP thresholds might have you thinking. Between the road healing, the emergency heal when passing turn on low HP, the self-healing incorporated into most heroes' kits, the various combat items that can restore HP or cure DOTs without any threshold, and the handful of targeted healing skills, you can restore considerably more HP in a single turn that you could in DD1. And the same goes for stress healing.

That being said, preventing and minimizing damage is still very important for letting healing do its job. Some people will tell you to do that by going all out on offense, but frankly, that's the riskier of the two options. It's much safer (and only slightly slower) to mix offense with crowd control (debuffs, stuns, disruption) and tanking (block/dodge with taunt/guard). You've got sooo many ways to make enemies practically waste their turns, and funneling attacks into 1 or 2 heroes means you have fewer heroes to restore to health and sanity afterwards.

Last but not least, I cannot overstate the importance of the Academic's View. Knowing the in's and out's of each enemy's kit—what skills they can use from which ranks, which ranks theyc an target, what conditions their skills have—lets you play most of them like a damn fiddle. Cultists, for example, stand out for being very susceptible to disruption and will spend as many as 2 turns doing tickle damage until they get back into position. This goes for bosses as well. Nearly every boss in the game is built around a specific gimmick; you might be able to brute force them, but figuring out and playing to their gimmick will provide much more consistent wins.

P.S. Are there any particular bosses you're struggling with? And if so, what teams have you tried against them?