To begin with, you need to purchase the "Additional Content" DLC packs in order to raise the level cap from 99 to 999 before you try to grind to level 999. (From what I'm told, the DLC characters start with 999 as their level cap regardless, but I haven't confirmed this.) You'll also need to download the Fairy Fencer F Collaboration DLC in order to gain one of the battles you need for this guide, but that's free anyway. You also need to unlock the Colosseum, which is a plan that must be completed.

It's also highly recommended to reach at least level 80-90 and get some Chapter 8 gear before attempting this. The best way to grind to this level would be to get to Chapter 7 or 8 and fight the dangerous monsters in dungeons as soon as you can reliably defeat them. One of the Chapter 7 Leanbox dungeons has a boss monster that gives about 600k EXP per fight (though it requires the Tough Enemies plan), so look around for a boss that is easy to beat while still getting good EXP.

Another bit of preparation to consider is finding red idea chips that give a Credit boost. If you can find a trio of Rank 5 Credit boost chips ("War", I believe) that is ideal.

One last thing: It's a good idea to wait until you gain all 12 story characters and unlock any CPU Candidates you want to grind before you get started. The more characters you have in your party, the better: everyone in the party gets XP, even if they aren't fighting.

Once you've reached at least level 80 (the game's recommended level) with some good gear for your main team, go to Planeptune and watch the event with Polytan. You'll start a "story" fight (game over if you lose) with 4 Polytans, after which you unlock the Polytan DENGEKI Fest! battle in the Colosseum.

The best bet to winning fights with the Polytans is to stack electricity protection and use AoE attacks if you can. After a certain level, MAGES. and Uni can two-shot the Polytans on the first turn with their most powerful AoE attacks. It'll take a bit longer without AoE, but as long as you have magic resistence (MEN) and electrical resistance you won't have too much trouble after about level 120.

Something to remember for all Colosseum fights: You start with full HP/SP for every fight, so don't be afraid to use SP skills! SP skills should be used before items in Colosseum matches, since you don't get your items back.

Why this fight is worth grinding:

Base Credit Reward: 50k credits + ~50k credits (battle results)+ ~50k credits (three Rank 5 Credit boost chips)
Total Credit Reward: ~151k credits + item sales (Real Angel Wings and Super Panacea sell for 2.4k per unit)

Base EXP Reward: ~2.4 million EXP (enough for 2 level-ups between level 100-400)

Once you've reached a point where you can take on the tougher colosseum battles reliably, you can move on to the next step to accelerate your grinding pace. (Or stick with Polytans for the 2000 fights you'd need to hit Millionaire achievement...)

Like the Polytans, this fight is against multiple oppontents so it's nice to bring characters with good AoE attacks like MAGES. and Uni.

Why this fight is worth grinding:

Base Credit Reward: 100k + ~740k (battle results)
Total Credit Reward: 840k + Credit Boost

Base EXP Reward: ~43 million (several level ups per character per fight)

As the other two before it, this is a group battle. However, take note that these enemies will try to inflict numerous status ailments (Poison, Paralyze, and Virus confirmed).

Why it's worth grinding:

Base Credit Reward: 100k + 1.6 million (battle results)
Total Credit Reward: ~1.7 million + Credit Boost

Base EXP Reward: ~68 million (several level ups per character per fight)

Bonus: AG System [material]
(This material is the only requirement for a quest that lowers the "Other" shares by a good amount near the end of the game. Great for clearing out the "Other" shares quickly in preparation for a True Ending run.)

It becomes much easier to grind these fights if you have the best gear available, but upgrading weapons can take millions of credits for small returns, especially for the CPU Candidates.

However, there is an alternative: many Colosseum fights give weapons as rewards, and some of the best weapons for CPU Candidates are only available from these fights. And since most of these fights are recommended for levels 90-120, they can be done quickly after grinding Polytans for a bit.

Note: The Colosseum fights for CPU Candidate weapons can only be unlocked through plans, so you'll have to fill out those plans before you can get the weapons.

Here's a list of Colosseum fights that give out the "best" gear (in raw stats) for certain characters:

CPUs

• Lost Image: Recommended Level 100, drops Mecha-Nep Blade (Neptune)
  
• Fear Purple: Recommended Level 100, drops Rune Caliber (Noire)
  
• Revenger: Recommended Level 95, drops Holy Duel Lance (Vert)
  
• The Lineage of '0' I: Recommended Level 85, drops W11-U Hammer (Blanc)
  
• Note: The initial Polytan fight gives you the weapon "Fury (Eryn)" for Neptune, which is stronger than the Mecha-Nep Blade in most stats.

CPU Candidates

• The Lineage of '0' III: Recommended Level 95, drops Hyper Beam Saber (Nepgear)
  
• New Beat: Recommended Level 100, drops Linear Railgun (Uni)
  
• Phantom of Time: Recommended Level 110, drops Melee Pencil -G- (Rom)
  
• Ruler of the End: Recommended Level 120, drops Metal Dogoo Pencil (Ram)

Makers

• Steel Spider: Recommended Level 110, drops Splashing Acid (Compa)
  
• Barring Wall: Recommended Level 85, drops Iffy's Qatar (IF)
  
• Lone Fang: Recommended Level 95, drops Taurus Rod (MAGES.)
  
• Moving Mountain: Recommended Level 100, drops Yuuga (MarvelousAQL)
  
• The Lineage of '0' II: Recommended Level 90, drops Magic Blood Twins (CyberConnect2)
  
• God of War: Recommended Level 100, drops B.K. True Deity (Tekken)
  
• Brave Wings: Recommended Level 90, drops Laughing Gema (Broccoli)
  
• Twinkling Star: Recommended Level 85, drops Annihilator (Falcom)

DLC Characters

• Note: These fights are difficult, even at the level cap. Also, there doesn't seem to be a Colosseum fight for Histoire's weapons, so you'll have to buy them.
  
• Beast who hunts Kings: Recommended Level 900, drops Noire Plushy (Plutia)
  
• Thunder and Lightning: Recommended Level 900, drops Star Gloves (Peashy)

Note: I was going to recommend fighting the Killachine in "Revenger II" (suggested level 700), but I decided against it. The unboosted credit gains aren't worth the fact that you need to use EXE skills to counteract its regeneration.

At any rate, grinding these specific fights should be a relatively quick and painless way to reach the DLC level cap and gain the Millionaire achievement (100 million credits). While it takes some grinding to reach the original level cap and it takes a few hours of Polytans before you can move on, it's easy once you can beat the tougher fights quickly. (I got from level 300 to 999 in about two hours of grinding, and got the Millionaire trophy along the way.)

Hopefully this guide helps a bit for endgame/DLC grinding, so you can spend more time tracking down materials for all the plans without worrying about being underleveled.