This is an endurance fight. Meaning, you have to deal with waves of adds in between dealing with the boss.
The fight with Septima Tharn is about pacing yourself. She fights you for a bit, summons minions, fights you a bit more, and then summons more minions, and then dies.
When fighting Septima Tharn, go slow and steady. Stay out of her ice ground AOE and just take your time damaging her so that you can stay high on your magicka resources. You don't want to end up low on magicka when she summons her minions. Once she gets low in health, then you can go all out. Now, I don't know for sure whether she summons more waves if you take longer to kill her, so a better strategy might be to do as much DPS as you can while Septima is out, and then kite the adds a bit to let your magicka regen. Now, Septima Tharn teleports a lot, so if you are using AoEs, be prepared for her to move out of them.
For the adds, there are a couple of methods.
1. Jump in, AOEs blazing, and burn them down. This method takes some DPS and probably isn't working for you. For this method, I'd use Conjured Ward, Power Surge, Wall of Elements and Liquid Lightning, and an ultimate that does damage to multiple targets. Again, this method is not the cautious method and probably results in deaths.
2. Kite the mobs. If you back up when the mobs come in, you can aggro them two or three at a time. If more aggro on you than you want, just back up or go into the water until they leash back to the "spots". This is slow but steady, with the goal being to break the mobs up into manageable groups. For a variation on kiting the mobs, use Line of Sight. Duck behind the pillars to break their line of sight. The idea here is that you don't have to confront all 10+ minions at once. By moving around and pulling smaller groups after you, you can deal with the minions in numbers that you are more comfortable with.
Deal the adds the normal way you deal with groups of enemies. I prefer to cast my AOEs, like wall of elements, liquid lightning, possibly boundless storm so that the enemies are taking constant damage before I switch to single target skills and heavy attacks. As usual, at low health switch to the Mage's Fury execute.
Depending on which Ultimate you are using and which phase is giving you the most trouble, you can use your Ultimate either to burn down Septima Tharn or the minions. Personally, I'd prefer Negate (Suppresion Field morph) or the Storm Atronach for this fight if using against the minions, or Storm Atronach or Overload if using it against Septima Tharn.
Last but not least, Damage mitigation. You want to be able to heal or mitigate damage in some way. Sorcerers have a some major ways. Power Surge gives buffs and a heal. Twilight Matriarch is a very good heal. Conjured Ward is an amazing damage shield that can compensate for relatively low health. Boundless storm give a solid amount of extra physical and spell resistance plus a small aoe damage. If you have sufficient skill in Light Armor, you can get another damage shield.
I hope this helps! These fights can be long and frustrating, but keep persevering.