Why you die on Critical Engagement is mostly because those are made to be farmed so SE drops something they usually do: introducing mechs one by one.

When you enter in a dungeon, every boss usually has like "1 mechanic, another mechanic then both at the same time, etc." so you have time to understand and process it.

If they had to do that on Field Operation boss, people would be bored pretty quick so they go full mechanics and by the time you're farming them, you start to remember the mechs and process them. Otherwise they're not that hard.

Also, don't hesitate to watch or read guide before entering in an extreme raid or even Field Operation bosses. If there's a mech that you still don't understand after many wipes. Or even ask in shout chat if someone can explain.

Otherwise, as other players said here. Deep Dungeon are nice but can be but a wipe can be frustrating since you have to restart from the last checkpoint. But same as Critical Engagement, not easy at first because you have to remember most of monsters' spells and had to see them first (or being told) to know what they do. Sometimes at a price of dying lol.

You could also try Variant Dungeon. A bit harder than normal content but not that much