You are bound to a new currency called Honor which depletes if you take any damage. When your Honor is at 0, you fail the Trial. That can happen even with the last boss, which means you'll have to do the entire Trial over again.
So — minimize the damage that you take as much as possible! Dodge roll everything, kite, and blast them with your skills. As stated earlier, hopefully you're confident in your build and damage. It's probably easier for ranged than melee.
There are some shrines that restore some Honor, so look for those on the map.
There are several types of rooms:
Ritual Trial: Kill two skeletons near portals that occasionally spawn a mob. The skeletons have a recharging shield, so focus them down relentlessly. Sometimes you'll see a room with just one big portal and four summoners.
Escape Trial: Timed room; run to each Death Crystal and click on them. After you click, watch where the light flies, as that tells you where the next one is. You don't have to kill monsters at all. It may be worth to click on the chests after you rack up some time.
Gauntlet Trial: A big room with traps and enemies, and gemmed gates; sometimes the gates are locked, but finding a Lever unlocks the doors, sometimes locking other ones. Look at the colors of the Levers and doors to see which ones are affected. Sometimes you'll have to backtrack to unlock the final door or proceed.
Hourglass Trial: Timed room; survive the fight with a Unique monster to beat it.
Look carefully when deciding on the next room; there are some particularly nasty debuffs that you should avoid at all costs, such as having reduced damage done by you or having the monsters deal more damage. You can also find Shrines that restore Honor, so you can get some back; it's priority to get to those unless you are quite full on Honor.
You also earn Sacred Water, which is basically like money during the run. You can use it with a Merchant if you find it on the map, but you can also spend them at the end. Remember to click on the fountain at the exit room of a Trial to get some. Sacred Water will probably matter more when you have to do longer Trials, but for now, don't worry too much about it.
The boss is a pain, because of tons of AoE damage around the room, so pay really good attention to the markers on the ground and avoid taking any unneccessary damage. It's actually not too bad to melee it, since it swings very slowly and in a fixed direction. So you might want to kite it very closely, even if you're ranged. Utilize all of the room as much as possible while doing as much damage as you can. If you haven't been good with your Honor, it may be too hard, however.
Don't get discouraged if you fail, it took me four tries to get this with a ranged Cold Sorceress. Get used to the Trials and kill enemies efficiently without taking any damage. You have to get a little lucky with Afflictions/Boons as well, as sometimes you can find some truly beneficial ones.
At the end, click on an Altar to choose your Ascendancy and spend 2 points. Use your keys on other rewards, as well.
How to get more Ascendancy Points in Path of Exile 2
Doing further Trials of Sekhema won't give you more Ascendancy points, unless it happens to have 4 trials on the coin.
Proceed into Act 3, and kill a Chimera boss; then you will have to find the Temple of Chaos to get the next points. Trial of Chaos is different from the Trial of Sekhemas, and you may find it easier.