best way to grind without raising battle rank?

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[PinkPаптҥэя]

To begin with, it depends whether you want to grind stats (HP, AP, STR, INT, SPD, UP) or skills/arts (e.g. Hexes: Poison Gas -> Paralyze Gas -> Smoke Canister, etc).

Grinding skills/arts is quite easy and can be done just by fighting long battles against single union rares, like Bai Ze. Even better if you lower your damage using an appropriate formation like Mystic Seal, Eremurus Rain or to a lesser extent Orb.
This procedure is effective at any BR, even against lower ranked enemies.

Grinding stat levels in an effective manner is more complicated.
First you need to get intimate knowledge of this wall of text:
http://lastremnant.wikia.com/wiki/Battle_Rank

It basically comes down to this:

• The best way to raise stat levels quickly is linking a huge number of enemies and defeating them within as few turns as possible. And we're not talking about linking 4 or 5 enemies, but 8-20 and defeating them within 10 turns less than the number of enemy unions !
  
• Thus the so called PC Ultimate Grind is the most effective way of gaining stat levels: http://lastremnant.wikia.com/wiki/PC_Ultimate_Grind
  
• The main problem is that you stop gaining stats as soon as your BR gets higher than the enemy BR. This will very soon exclude common enemies as grinding targets and only leave you with rares.
  This means that the PC Ultimate Grind will only work effectively as long as your BR is somewhere below 20, else you will only gain some skills, but no stat levels!
  
• Also you need to apply all the BR reducing techniques laid out in the Wikia's BR page, like getting 25 units KOs. This is not quite easy with the landworms, but sometimes can be done using DEF reducing formations, like Belt or Porcelain Chain.

If your BR is higher than 20, you're more or less only left with the Lavafender Grind up to BR 30-35, grinding Spiritwoods in Numor Mine: Op. Area 5 up to BR 65 or much later grinding Oblivion Wings/Observers in the Ancient Ruins.
I recently wrote a Steam Guide for TLR, where these grinding techniques are explained:
http://steamcommunity.com/sharedfiles/filedetails/?id=531214170