I know this has popped up in quite a few places (and virtually almost done to death), but I'm just here to share some ideas for the CO, MINUS Tinkinzar (that I'll leave to OOO to worry about).
I'm also not going to suggest where you want to put them in, because as of now OOO also has plans underway for the Core. Would prefer them as enemies with their own levels, though.

General Suggestions
The Crimson Order gremlin enemies would have their own unique set of armors and face masks, and an insignia of the Crimson Order. Essentially its identical in design to the Gremlin insignia, but crimson with a black background.
These enemies are essentially very strong versions of normal Gremlins, and will have several specialized classes too.
Each Crimson Gremlin, except for the Crimson Officer and Assassin, has a more powerful version known as Sergeants, and has a low chance of spawning with regular Crimson Gremlins.

Encounters
Each Crimson Order encounter usually has one Officer, surrounded by two Snipers, one Obliterator, one Engineer, and about 2 to 4 Legionnaires. The Legionnaires normally stay close to the Officer. It's usually a good strategy to get rid of the ranged Crimson Gremlins before the Officer, unless the Officer is defending these Gremlins.

Alternatively, two to three Crimson Assassins may be encountered at once.

Crimson Legionnaire
Description: Few Gremlin Thwackers make it into the honorable positions of Crimson Legionnaires, the royal guards of the Crimson Order. They protect and serve King Tinkinzar, but more importantly pledge their allegiance primarily to their Officers.

Essentially, these are very heavily armored Thwackers, carrying a sword in one hand and wielding Strike Boosters on their backs - allowing them to dash away and evade attacks at phenomenal speeds. They don't need shields - their armors are so thick, piercing through them is already a challenge. Swords wielded by these Gremlins can range from Divine Avengers, Gran Fausts or Triglavs.
Sergeants gain two additional, very deadly abilities. With their modified boosters, they can unleash a powerful sonic blast from their boosters that immobilizes all Knights momentarily. They can also use their boosters to dash towards a Knight at very high speeds, stunning the target and dealing immense amounts of damage. To make matters worse, Sergeants' swords are always Dread Venom Strikers.

Crimson Officer
Description: Almost never seen by Knights, and highly ranked in the Crimson Order, Officers command a great deal of respect, and instill a great deal of fear. They don't need to engage in combat, but they certainly aren't something to be neglected.

These Gremlins are slightly taller than the rest of their brethren, and their only offensive capability is relying on a revolver that looks suspiciously like a Sentenza - and only occasionally.
Rather, their other skills define how deadly they are. Each Officer can expand a powerful force shield that pushes back all Knights and renders Gremlins inside the shield immune to damage, just like a Guardian in Lockdown. Unlike Guardians, however, the shield stays up only for a few seconds, is indestructible, and shocks all nearby.
They can also area heal and resurrect Crimson Gremlins.
Killing an Officer causes all Crimson Gremlins in his battalion to focus their attacks solely onto the Knight who last attacked the Officer.

Crimson Sniper
Description: The sharpshooters of the Order, Snipers back up the Legionnaries in taking out targets too far for them to reach. Generally found hiding behind their more durable counterparts, Snipers can become a formidable foe if not taken care of quickly.

Their rifle shots are impossible to dodge, and very difficult to block given that they fire suddenly and rapidly. Luckily each individual shot doesn't deal a whole lot of damage, but they can whittle down your health gradually over time.
If a Knight gets too close for comfort, Snipers teleport out of the way, making hitting them with a sword merely a test of reflexes. The good news, however, is that they cannot move when zooming in to their rifles.
Sergeants become a much bigger nuisance as they gain a cloaking shield that renders them invisible except when it glitches occasionally. Their shots also deal a substantial amount of damage against Knights, and they teleport after every shot taken.

Crimson Obliterator
Description: Demolition experts in the Order are generally enlisted as Crimson Obliterators, and given a far more lethal weapon to wield - a rocket launcher. True to their namesake, nobody has actually managed to survive one of their rocket hits.

Their homing rocket attacks can make your life very difficult, though unlike the Sniper, they are much less mobile. Get close to them, however, and they will whip out Gremlin Demo bombs to scatter all around them.
Sergeants can fire rockets that create a field of fire wherever they impact, and generally fire at a much faster rate than their lower-ranked counterparts.

Crimson Engineer
Description: The few technologically adept Gremlins that have little experience in actual combat are sent to the field as engineers. While they may not pack a punch on their own, their unique creations are certainly a force to be feared, turning this whiz into a one-Gremlin army.

Engineers are able to attack, but can assemble and summon up to three constructs at once, not to mention repair them. Each unique construct has a special ability and is branded with the Crimson Order insignia:
Mecha Knight - Each Mecha Knight has a charge attack similar to Lockdown Strikers.
Retrode - They can fire beams in 2 directions at once.
Scuttlebot - These explode upon death.
Engineer Sergeants can also create a shield around one of these constructs, making them invulnerable until the engineer is killed. Each sergeant can summon up to 5 constructs at once.

Crimson Assassin
Description: The most feared of all the Crimson Order, Assassins previously dealed with dissidents within the Order, ensuring that all are loyal only to King Tinkinzar. They dislike working with the rest of the brethren, and are already a formidable force on their own.

Perhaps the most dangerous of all the Crimson Gremlins. Luckily for you, they do not spawn with Officers, and only operate in pairs or threes.
They primarily dash around at very high speeds, and circle their targets before attacking. They teleport almost instantaneously when approached, and normally enjoy teleporting to the backs of Knights, where they will dish out very high damage with their double daggers (if a full combo is dealt - i.e. 5 hits, they will deal up to 25 bars of damage, so watch out!)
After teleporting, there is a very short window of time before they teleport again, so be quick enough and hit them once or twice before they do. Essentially a battle with Assassins tests your reflexes.
Alternatively, they can throw knives at high speed while dashing, although this does extremely low damage.

Images coming soon, but in the meantime do post feedback and add on with your own suggestions~