Keep moving
Mobility is key in Doom Eternal, and it's even more true when it comes to Slayer Gates. Especially on higher difficulties enemy attacks will take huge chunks of health away from you, so you'll want to avoid getting hit as much as possible. Stray Imp fireballs and other projectiles are much more likely to connect with you if you're still, so use the Doomslayer's immense speed and agility to consistently outsmart your opponents. Stay in the air when possible and use your dashes when you can. The more you move, the more likely you are to survive. Keep an eye out for health and armor mics so you know where to retreat when things get hairy.
Use Flame Belch frequently
Slain Glories are the primary means of healing in Doom Eternal, but they only grant health, not armor. Tons of Doom Eternal players ignore Flame Belch's ability, which supplements glory kills by supplementing your armor instead of your health. Not only does Flame Belch fulfill a valuable resource, but it's also a great crowd control tool that excels at taking out large groups of weaker demons. Killing a burning enemy will cause them to explode with pieces of armor, which could very well save your life in a killer gate. With this tool, you can essentially turn large crowds into armor generators, popping them like flaming piñatas whenever you need a little helping hand.
Upgrade your equipment
Sometimes you just aren't quite suited for the job. This does not mean that the task is impossible. It just means that you are ill-prepared. Fortunately, Doom Eternal offers several methods to improve your skills and abilities so that you can come back even stronger. Make sure you have the best runes equipped for the situation, and go out and find Sentinel Crystals to increase your max health, armor, and ammo capacity. You can also install Praetor Suit upgrades while you're at it, too. These upgrades will give you the extra edge you need to dominate demonic hordes in whatever Slayer Gate gives you trouble.
Constantly swap your weapons
Once you've got your hands on all of the weapons in Doom Eternal, it's easy to stick with your favorite. Sometimes it is difficult to replace the Super Shotgun. Still, using your entire arsenal is paramount for survival in Doom Eternal, so be sure to switch between all of your weapons frequently. Each weapon in Doom Eternal excels at a different purpose, and while you can diversify certain weapons with certain weapon mods, one weapon cannot handle all situations. Use the rocket launcher to quickly dispatch tricky demons that give you a hard time. The heavy cannon and ballista are great for taking out this long range annoyance. Hunting rifles are wonderful for close range combat. Keep juggling the weapons and you'll be fine. Add a chainsaw or two for good measure.
Come back later
Sometimes you're just not in the right headspace for a Slayer Gate. Just like in a puzzle game, relentlessly engaging in a challenge can lead to decreased results, and you might be able to clear it on the first try if you come back later. Also, if you aren't equipped, you can take some time to go and acquire upgrades and new weapons before giving Slayer Gate another shot. Continue the campaign. Learn new tricks and practice what you already know. The additional experience may come in handy when you return. All in all, sometimes it's best to just walk away from a Slayer Gate and come back with some additional knowledge and experience.