Let's get straight into it shall we?
Ok, first things first, I'm going to use massive for image examples for what I say, just because it's so commonly used, but whatever I say should be translatable to pretty much any other subtractive synth out there. (Most of my euroleads are actually made in Sylenth)
Alright, so the basic sound your going to want to work with here are supersaws. These are basically well, sawtooth waves layered over each other, and slightly detuned so that they phase. The amount of voices and the amount of detuning is all up to you.

This is basically how I'd do it in massive, one normal wave, one tuned up slightly and one tuned down slightly. In Sylenth, I would have two saws on both parts of both part A and part B, and have part A slightly detuned using the detune option and the fine tuner, and part B be slightly more detuned on those two aspects. There, you already have the basic supersaw sound you'll want, which can be changed around with effects of your choice to make it sound less bland.
The other important characteristic of a Eurobeat sawtooth, is that "hitting" kind of "brassy" sound, I guess, which comes into place using envelopes.
In massive, what I'd do is make one osc an octave down, one osc an octave up and chuck envelopes on both of them, bringing the, back to the original octave, and using the attack to give it the hitty sound. (The speed of the attack really depends on what kind of eurobeat you are making).
If what I said didn't make sense, here, have a screenshot of the envelopes.

In Sylenth, I would do something pretty much the same but only slightly different. I would actually use the decay part of the envelope to move the pitch, and have the attack on zero. So basically, I'll have the envelopes on the pitch of part A and part B, making the decays move one of them from up to down and the other from down to up. the amount the pitch is changed and the speed is again, entirely up to you and what you think sounds right.
Also, note that this is just the basics, many Eurobeat sawtooths do not sound the same. To get a more unique sound, you could try layering it with other leads, playing around with the detuning, playing around with various effects, heck, I even tried layering the sawtooth with a supersquare and it sounded pretty cool!
I might do a more in depth tutorial on the genre of Eurobeat itself later if I find time, but I hope y'all find this guide useful for now!