Thanks for writing this up, it helped me find a real problem! legendaries aren't immune to spikes, but in your game they were practically immortal, and the reason is healing. Brann heals his party, and regular clerics walking next to them heal them too. Healing is a percentage of max health, and legendaries have up to 10 times the health of a peasant at the same fame, so one cleric nearby heals them faster than a whole row of spikes can hurt them.
A few things that should help right now:
Mud right before fire. Mud slows them down and leaves them "muddied" for 2 seconds: they take 30% more damage from everything (more with mud upgrades), and fire burns muddied adventurers 2.5 times harder. Without mud, fire is basically a strong spike. Try changing your three tiles to mud, fire, spike, with the mud on the tile they step on just before the fire. In my test without healing, your current layout left them at 25–55% health when they reached the core; with mud before each fire, all four died before the middle of the path.
Slimes don't stop them. Legendaries crush any monster in their way with one hit. Slimes are great against the crowd, not against the party.
Core health doesn't help against them. Each legendary that reaches the core takes about a third of its max health, however many upgrades it has, so three of them destroy it. That mana does more in traps.
The party is meant to end a life. Each legendary you kill gives you a title, and when you reincarnate, titles make you stronger for good (Ancient Arsenal makes every trap hit harder). Fame 15 is about normal for a first life; the next ones go further.
You're right that the game doesn't tell you how strong the traps are or how much health adventurers have. I've noted that, along with aiming the auto pulse at the party. Thanks for playing!