Cult of the Lamb

Note: to fight any boss again after defeating it the first time, reenter the boss's area. Then, at the start of any combat stage (ones marked with a sword icon) there will be an idol statue with Devotion you can steal. Destroy the statue to reveal a teleport pad below it. Use it to be taken directly to the boss fight again.

While each boss has their own attacks, the actual strategy for defeating each without taking damage is actually the same. Note that the achievements require you to not take damage, not to beat the boss without getting hit. If you happen to have the tarot card that gives a 10% chance to negate damage when getting hit, you could potentially get hit and have that card proc and still get this achievement. I wouldn't rely on that though.

The basic strategy for every boss fight is the same: roll in, hit the boss multiple times, then roll away when the boss is about to attack so you can either avoid it or dodge through it. Leshy goes underground with spikes, and Heket jumps with a shockwave, so both of those you'll want to hit a few times then roll away to avoid damage, then roll back in and hit them some more. For all four bosses though, if you're confident enough in your roll dodge, you can actually just stay right next to them and roll dodge to avoid all of their attacks. If you practice enough, this is feasible, but it's safer to just roll away and come back.

Speaking of safer, that's really the main thing to get these achievements: be patient and play it safe. Roll in, get a couple hits, then roll away. If you get greedy and aggressive, there's a much higher likelihood you'll accidentally get hit, or be in the middle of swinging and can't dodge cancel to roll out of the way. Because of this, I always found that faster weapons were better than the slow and strong hammers and axes. With fast hits, you have plenty more opportunities to roll away if need be, rather than being locked into a long and slow attack.

One other thing to point out is that each boss has two great opportunities to just wail away on them. The first is when they just shoot out enemies or vertical projectiles that just fall to the ground in marked spots. You are virtually always safe from these attacks while right next to the boss, so just stand there swinging at it over and over while it's doing these attacks. The other time is when the boss switches into a final phase of some sort. For example, when Heket is down to around 30% health, it'll jump to the center of the screen and then jump off screen. While it's doing this, you can stand next to it and hit it a lot, sometimes even finishing the fight before it can do this final phase. The same goes for Shamura when it's slinging itself away and back. Take both of those opportunities to do a ton of damage to each boss.

The final thing to address is the adds (enemies the boss spawns). I personally ignored them in every fight. Fighting them will take your attention off the boss and likely result in you getting hit. I found it easier to just rolle around and kite the enemies away from the boss, or just roll in, attack the boss, and roll out, and the enemies weren't fast enough to catch me. Fighting the enemies just opens you up for them to hit you too, while you're fighting them. So I recommend ignoring them.

Lastly, don't forget that you can wait for these achievements unlock you've gotten all Sermon upgrades for your weapon level and the different types of weapons. The first bosses will die very quickly to max level weapons, so I recommend not even bothering with these achievements until you have leveled up your weapons most or all of the way.