You might consider using Pistols as your primary weapon to make things easier. I have one character who completed all the solo content as a Pistol primary, and another character who did it all as a Chaos Magic primary, and Chaos was definitely more of a grind. As you may have already noticed, Chaos single target attacks are a little behind other weapons in dealing damage. The other Chaos skills are very useful, but generally the fights that go longer and drain you of energy are going to be fights against 1 or 2 targets, making single target attacks more important for your primary slot weapon, which regenerates energy faster. Spending energy on group attacks isn't efficient against less than 3 targets.

Pistols also have my favorite group attack, the 3 energy one, because you don't have to worry about a cone of fire or an area of effect, it just auto-targets everything, so you never waste time herding or waste an energy point. You just fire away, it always hits. I'd say in general that 99% of solo content is easiest played as a DPS race to 0 health, and Pistols are just flat out better than Chaos magic at that.

So with that in mind, I might go with Hair Trigger (basic), Controlled Shooting (3pt group) and Shootout (5pt single) from Pistols, and Pandemonium (elite) and Breakdown (5pt single) from Chaos Magic. I know I just said Chaos singles are bad, but if a fight goes long enough to burn through all your primary weapon energy, it's probably against a single target. For the final slot, your choice of Evulsion (interrupt), Clean Slate (healing) or a Chaos magic AoE if Controlled Shooting + Pandemonium isn't killing off groups quickly enough. For Passives I'd take all the skill-linked ones except the last slot, where I'd take Resonance Cascade from Chaos (1st column, 4th row). It's a nice, brainless bonus, but maybe not as useful with Chaos in secondary now that I think of it.

Lastly, consider equipping a Cold Silver Dice talisman. With Shootout and Breakdown both being multi-hit attacks, you have a better than usual chance of getting a crit to trigger the energy point bonus. Also plan to wear 4 +crit glyphs, 1 accuracy glyph, and at least 2 crit dmg glyphs. Always prioritize attaching glyphs to talismans over weapons, because weapon glyphs only trigger when using that specific weapon. And I personally almost always have Anima Allocation at 100% damage, even with my tank character when it isn't tanking.

My guess though is you more likely have a gear upgrade problem than a skill problem. It's really hard to go too far wrong with skills, and what I'm proposing is only going to be a little more efficient. My characters also don't use the best extraordinary weapons (too expensive) and still didn't have much trouble, so don't worry about that holding you back. You just need to keep those talismans upgraded, and don't settle for less than 3 pips except on Cold Silver Dice, certain weapons and (early on) crit glyphs.