Flame Mammoth's stage is slightly different between any% and 100%. 100% has more potential time-wasters than any%, with the items you need to gather, while in any% you just blast through everything. Even the boss fight is pretty easy. Something to keep in mind is that, in general, you want to dash along the surface of conveyors going to the right, as those add to your speed, and dash jump along conveyors going to the left that are working against you.
The easy way through the first section is to go beneath the second set of conveyors (after passing the sky claw). Taking the top route saves time, and can be done multiple ways. Using c.sting allows you to dash along the full length of the final conveyor belt, while using ice you'll have to jump off before the final enemy drops. Ice is more simple, since well timed shots will kill both types of enemies that drop down onto the conveyor belts. You're aiming to fire an ice shot early so the enemy drops right on top of it, forcing ricocheted pieces to hit as well. C.sting only needs one precise shot, though, on the final enemy (in case it's an utuboros head). The blue guys that drop die in 1 c.sting shot, while the utuboros heads take two.
The next section is very simple, just dash to the right, climb onto the platforms in front of you, and use c.sting (or a few buster shots) to kill each miner in your way. A short climb brings you to the next conveyor belt section. Dash along the length of the first conveyor belt, but don't dash along the second. Despite moving to the right, the lag caused from kicking up dust sprites more than outweighs the benefit of the added velocity, so it's faster to do dash jumps to avoid causing lag.
Just keep dashing and jumping through the next section, as long as you time your jumps to avoid slamming into the couple spikes that are in your way, you don't have to worry about getting hit by the pipes dripping.
There's one tricky section at the end, getting around a green guy on a raised platform. The easy way around is to do a dash wallkick off the wall beneath him and let that jump carry you over him before continuing on. The difficult way is to land right in front of him and dash jump over. Doing so makes it very easy to just dash into him, or get the spacing slightly wrong. It's also possible to not jump far enough and crash into the spike behind the green guy, but it doesn't waste much time to attempt, and saves a significant amount of time.
Without c.sting, this stage is a bit different. If you want to take the top route of the first conveyor belt section, it has to be done with properly timed ice shots (as described above).
The jump to break the blocks leading to the buster upgrade can be done if you break the bottom right block and fall, but not if you break both of the bottom blocks, so be careful. If you find yourself stuck wallkicking without breaking any blocks, you can try sliding down and actually slipping off the block you're on, then quickly pressing jump again. This will get you to catch the next column of blocks over (or the wall) and will let you up more easily. There is a risk of falling if you do this, so practice a bit before attempting it in runs, if you break the bottom blocks and fall your only options are to revisit the stage or commit suicide to try again.
Start charging up your buster and switch to ice after you get the upgrade. Drop the ice sled on the left edge of the next platform (killing the miner blocking your path). Stand on top of it and jump to the left. Make sure not to go too far left and just bonk your head on the ceiling, but you do need to get close to the wall. Hit jump again when you reach max height and when you're close to the wall (remember you can wallkick from up to 7 pixels away, so you can just be close) and you should kick off the wall so you can reach the subtank. From here, the iceless vs no-iceless routes diverge in getting the subtank and heart.
After getting the two items, proceed like in any% on the conveyor section. After it, start charging and swap to ice. You can use charged ice to kill the green guy on the raised platform near the end of the stage in one hit and get by without any risk of bonking.
Without iceless Edit
Break the 2 lower blocks, get inside the gap you've made, right up next to the left column of bricks, and jump. You should be able to break all of the blocks this way. On your way out, you can wallkick off the wall again and you'll miss the miner in your way, or you can try using a charged weapon to kill him before you run into him, or even just jump the right height on the way out.
After getting the subtank, charge up and switch to tornado, kill the middle miner as you approach the heart container, if you don't he can throw a pickaxe and hit you with it. Climb the walls on the right and you'll be to the next conveyor section.
With iceless Edit
You can grab the subtank without having to break through the blocks with the boomerang in a couple different ways. The simpler way is to climb up to the level the subtank is at and throw the boomerang directly at it. A slightly more difficult way is to swap to boomerang right as the ice sled despawns and fire a boomerang that will curve upward and grab the subtank.
Grabbing the heart with the boomerangs is a bit tougher. The setup is simple, on the last platform before the right wall, there are 3 miners. Jump over the second one. You want to stop short just in front of the miner during your jump and fire a boomerang right over his head. It should curve downward and grab the heart. If it doesn't quite reach, you fired too high.
Mammoth fight Edit
It's faster to hit Mammoth with a buster shot at the start of the fight because tornado travels slowly. Make sure to dash through the door leading into the boss room, so you can get the first shot on the boss more easily. If you're at dash speed when you lose control of X, for some reason the game isn't aware that your dash came to an end, so if you just fire a buster shot at the start of a fight, it will count as a dash shot. This allows you to just spam shoot as the fight begins and get the shot in before he jumps. As a backup, when the fight starts just dash jump and shoot him in the air, it isn't a huge deal to miss the first shot by a little bit.
After hitting him with the dash shot, swap to tornado and fire from close up so you can get 2 hits in per tornado. His attacks aren't too difficult to dodge, just try to get into position to shoot again as your tornadoes go off screen. Even if you end up taking some hits, there shouldn't be any danger of dying.