It's a gear problem. What main stats do your gloves, chestplate and boots have? And what other items do you have to replace them, if possible? 

When looking for other items, you should include stuff used by other champs. A typical mistake when starting at Raid is, spreading your good gear among to many champions, so in the end none of them is really strong. The campaign farmer has to work first, give your actual best gear to Athel.

You will probably not use a lot of the stuff that is your best gear now in the future at all. Early on, you have a lot of 4* gear, like everybody had at the start. Later you want to equip all champs with 6* gear. But for now, give Athel the absolute best stuff you have, even if you have to steal from other champs.

I mean statwise I can find better individual pieces from these, but then I lose the lifesteal, which helped a lot til now. I feel that it help less and less as I progress, but that was the reason I was hesitating. Also crit damage gloves, attack% chest which isn't a go-to, i know, it was only the best piece in lifesteal, that's why it's on her, and speed boots

I think you should get rid of the lifesteal set and increase her atk and crit damage instead. If she kills Lord Shazar in round 3 with one attack, there is no need for lifesteal anymore. Dead enemies don't deal damage to you.

If your masteries are causing the problem you could revert them back. Clan boss isn't going anywhere. :) Lifesteal are probably still essential to you.this early game. My Athel also sometimes gets killed by the double bombs, but it's not common for them both to land, just unlucky.

I mean, I really want that Hard CB reward chest, and without Giantslayer, it's a big nono. So I think the only solution would be getting better gear somehow?

My Athel has similar stats to yours, including the bit to low crit damage (112 compared to your 92). The only really big difference is, that my Athel has 1000 attack more than yours. That's enough to onsehot any wave in 12.3 brutal with an atk buffed A2. Wave 1 AoE kill. Wave 2 with the A1 attack only. Wave 3 AoE kill. 100% success rate. No life leech needed. 

Maybe a little bit more speed in addition to the attack, so you can go twice in wave 2 and take down 2 enemies before they have a turn.

You always look to upgrade your Resistance in the Great Hall, for blue Magic affinity champions, such as Athel. :)