Make no mistake, Battletoads hates you, but there are ways you can even the field a bit.
Like in Stage 1 for instance, if you're fast enough dispatching the first two enemies (and you have to be really fast, under 10 seconds fast), you'll notice a flashing area up on the first platform on the right.

If you can touch it, you'll be warped away to level 3, a.k.a. the Speeder Bike level


The main drawback is that you will have skipped Stage 2, and will have missed the opportunity to stock up on some lives there, but you have alternate methods for that anyway.
The Battletoads games are hard. So are the Double Dragon games. Mash them together for whatever reason, and you get a game that's also pretty tough.
But you have a secret weapon.
If you go to the Character Select screen

Then press
B, A, Down, B, Up, Down
You'll hear a noise. Finish selecting your character by pressing Start and behold!

The Super Warp Zone! Which also gives you five lives to play with.

And you're going to need every one of them.
I've mentioned it before, but it bears repeating, Battletoads is a tough game. And you can take certain measures to pad your lives a bit, but you'll find out pretty quickly that you need more.
So, make your way to Level 2, the big tree-thing. And find these weird silver bugs with stingers.

They only take one hit to defeat, but they kind of bounce up when you hit them. Hit them again when they bounce off the wall. Then hit them again and again until.
1up!
Once they give up the 1up, they fall down off the bottom of the screen. And you can do this once for each of the bugs that you find in the tree.
Just be warned that the other bugs can sting the one that you're bouncing off the wall and if they get the last hit in, you get nothing.
There's no way around it, Battletoads is a tough game. Those three lives you get at the beginning of the game start to look insufficient pretty early on.

But, you can give yourself a slight edge.
At the 'press start' screen you can hold Down on the control pad + A + B and press Start. Then you'll have five Toads at your disposal instead of three.

And, yeah, this works for the Super NES version also.

In the first level of the Super NES edition of Battletoads, you have two parts where you're pelted with Hot Flaming Death From Above via a couple of volcanoes in the background. you have to keep moving in a zigzag pattern or they'll smack you right in the head. It's like they know where you're going to be.
Weird.
Well, they do know... sort of. It appears that the fireballs will take into account the direction and speed that you're going and land directly in your path. Sneaky.
But, if you get behind a chunk of scenery and run into it, you can trick the game into thinking you're running one direction or the other, but since you're not actually moving anywhere the fireballs will harmlessly explode right in front of you.

Just like that. This even works in two-player mode. Just make sure that both of you are on the same side of the scenery running the same direction. Otherwise you risk KOing your buddy... which might actually be pretty funny.