Sure, you can ask for recs here. (And anyone is welcome to give them if they like, not just me!)
In any case, sure, we have action-adventure fics along the lines of what you describe. The one that first springs to mind is
The Legendarian Chronicles, which is about kids caught up in a prophesied battle between legendary pokémon and humans. Naturally you get a lot of nice big battle scenes with legendary pokémon going all-out against armies of enemies, with the human characters having to learn to fight against incredible odds and use strategy just to survive in dangerous fights.
Requiem would be another good story to look at in that vein; plenty of action with emphasis on how the attacks affect the battling pokémon as well as the environment. The power level on this story is very high, so by the end there are battles with legendary pokémon throwing skyscrapers around, etc. It's also complete.
If you enjoy PMD fics, most of the ones we have around are action/adventure stories that would probably be to your taste. Of the more established ones,
Guiding Light is probably the fastest-paced with the most big battles, often with unusual environmental conditions that change how fights play out.
System: Reboot is very action- and battle-oriented and worth checking out if you enjoy sci-fi, but most of the battles are with space weaponry rather than normal pokémon attacks, so it might not be quite what you're looking for there. On the other hand,
Fledglings has nice battles, but the overall pace may not be as fast as you're looking for.