Ideas: Dangerous Enemy

You could use some simple tricks to get this effect, like having few characters apart from the villain refer to you by name. In addition, you might want to have the villain turn up in various maps and check-points that you would need to cross on your journey.

If you give them a team that will be effective against most Pokémon you include in the early-game, then they will come across with more impact. Having them refer to the player's quest or journey, as Sephiroth often does in their own way, would be effective. Villains who don't seem to notice that the player is on a journey might not seem as directly threatening.

That said, if the villain is a major part of your game's appeal, do you want the player to defeat and attack them? The game would seem to rather preserve them. The villain is a force which improves the game, not one to be disliked. Alleged genres like 'dystopian' which are defined by their 'villain' often also fall foul of this - such stories can easily seem ungrateful. Still, you might want to either have the 'villain' win, as something of a cop-out, or not have the centre of the game be something to be disliked. A dangerous villain is still a positive step.

Apart from that aside, try to have them attack in enclosed or suffocating locations. Villains who attack in wide, open spaces, as in R/S/E, can often come across as more akin to a quest where one attacks them freely. Instead of them attacking you, you attack them as part of your 'heroic' journey. You might prefer the sense of danger that can come with villains who attack in locations where there's no notable way out. Alternatively, you can end by combining them slightly like Mewtwo does in the film - he lures the trainers into a trapped area, but in there acts as if it's a formal event and gives them space, introduces himself, etc. Mewtwo hence distorts the usual format of such events and space in the Pokémon world, and it becomes a highly threatening context. At the same time, he is strict about the rules and tries to avoid directly interfering in Pokémon battles or attacking the trainers, while if he was more directly aggressive (apparently the Pokémon are alright with the destruction of other areas but one person being harmed is too much for them. Precious little things. This kind of thing in the anime can seem slightly parodic.) Hence, the terrain and setting they attack in is important.

Finally, you might want to take a leaf out of Pokémon games which aren't core-series, and give the villains 'special' moves which only their Pokémon will tend to use. This can be done either by giving them rare or 'shadow' versions of Pokémon, or just by directly giving their notable trainers the moves. This will help focus the game around them.

Edit: As a note, a long forum post (or paragraph) is like a closed location, and a short forum post (or paragraph) is like an open location. It doesn't hold readers up or separate itself as much from other posts. Hence, long posts can easily be atmospheric, etc., as well - short posts often adapt too easily to the atmosphere surrounding them. So that might help you get a sense of enclosed locations, etc., and how they can be taken further than just basic location design.