Okay, sure!
I feel like we're detracting from the original point now, being X Sonic's underwater movement. If you're willingly not using the tools at your disposal, then of course it's not gonna feel great to play. With Ring Burst it can be understandable due to lack of rings, but even then you have other options to get through or out of water.
Regardless, If we're eliminating both Bubble Shield and Ring Burst usage from Azure Temple, then yeah it's going to be near impossible, but at that point, it's more on the fault of the player for not utilizing all of X Sonic's moves, and not the underwater nerfs.
If we eliminate just Ring Burst, however, then yeah the stage is clearable. Really the main hurdle here is the split paths at the beginning before the first checkpoint. If you pick up the Bubble Shield by kicking the gargoyles at the beginning, you should be fine. After the first checkpoint you can ditch both of those and still complete the level. Even on the upper or lower path. You'll struggle if you do this sure, but again, it's on you if you do that.
Want an additional tip?
You're invincible to a lot of things when using Ring Burst, and this includes the projectiles the gargoyles shoot.
You can also Snap Dive off the gargoyles. Not so much their projectiles though.
Azure Temple mostly comes down to learning the projectile cycles, where they shoot and in what pattern. If you're having trouble, don't be afraid to just stop for a second and learn when to go. You can't always brute force this. Snap Dive can also keep you close to the ground if you're worried about being hit by the upper projectiles.
View attachment 139889