This is one of the hardest achievements for the game. Since the latest patch, it became a lot more difficult. However, it may be easier than it seems if you make the right preparations. Unlike other guides, I will start the solution on things you need besides the fight with Gargos itself.
First of all, there is much to do before the fight with Gargos. Preparing yourself right is the key. You don't have to worry only about him, but also about some fights until you reach him, plus the four Omens.
What I recommend you do before attempting Godlike:
I - Preparation
1 - Unlock Eyedoll
Eyedoll rocks against Omens. Even if he is not a guaranteed win against Gargos, he is also good against him. But the best use I had for him was to take the four Omens with ease. They are a medium difficulty fight only if you know their movements, have the right setup, and bring Eyedoll.
For unlocking him, you first have to beat the game. Then, a new set of missions will appear. There are seven in total. Two of them you need to answer a question correctly. I don't remember exactly the questions, but they are literal, not metaphoric. First answer is "stars", second one "passing of time". After doing all seven quests, and trusting Kan-Ra when asked, you bring Eyedoll back to live. Oh, be careful in the battle against Gargos' Champion. It is a really though fight. Go for it with all you have.
Once Eyedoll is created, there will be new quests for actually fighting him and convencing him to join you. You must defeat him four times, each one with him more powerful than before. Every time there is a choice to be made in these quests, answer in relation to bringing him to your side. The last fight against Eyedoll is also pretty hard, so don't spare anything. The Riptor and Rash strategies I mention later are a good choice for the fight. After all that, you will unlock him.
All this is optional, but I highly recommend doing it.
2 - Make sure you have plenty of resources
For resources, I mean all resources you are going to use.
Just go to the fight once you alredy have all the best guardians bought, astral energy for them, and healing and reviving items, plus the items and consumables for the fights. Don't count on getting ANYTHING on Godlike.
The setup I used is simple, and this is what you should aim to have.
Eyedoll with Killer or Carmesin Astral Tiki; Riptor with Killer or Carmesin Fractured Ward; and Rash with Killer or Carmesin Snake (did not use him that much, actually).
For the Gargos fight, all of them had Pickled Rodent Brain as consumable, and entered the fight full of instinct and shadow meter. Remember to farm items for filling the meters as well.
For artifacts, all of them had Myogene and Dragonskin Nanobots level III, plus the lizard foot (the one that makes your opponents attacks drain their shadow and instinct meter). For Riptor and Rash, I also used the perfect mummy talisman for damaging Gargos automatically.
Besides that, I used around 10 25%healing scrolls, plus three revivals, I think. I think I used around 2k astral energy more or less. Be sure to have a good stock on all this items before trying. Every time I failed, I would make sure I had at least this before retrying. If I had not, I would go to normal and farm.
3 - Train against Omens and Gargos on lower levels until you know how they fight
Omens and Gargos have a similar way of fighting on all levels of dificulty. Of course, on Godlike they are much harder, but some things are the same. Before I finished the game on Godlike, I finished it four times on Normal and two on Advanced, for training. I also failed three times on Godlike (that is training as well, right?). The training really did a difference for the last and winner run.
II - During the campaign
You want to have as few fights as possible, but you also want to manage the corruption, so it goes up quickly, but one place at a time. YOU WANT TO AVOID HAVING TWO OMENS AT THE SAME TIME, TWO IN SEQUENCE, AND ABOVE ALL, HAVING GARGOS BEFORE TAKING THE FOUR BUFFS AWAY. I can't stress this enough, specially the buffs. Gargos can only come after you take all the four buffs.
At first, start skipping turns and let the corruption rise. If you have to do a fight, you can try go simulate it, or do the easiest one. You want to do the fights that, if not done, would result in one from the three situations above. This means you will have to fight sometimes, and actually win. Just take your best character, probably Riptor with the strong punch glitch, your best fractured ward guardian, and go for the win. That is what I did.
If you manage the corruption correctly and you are lucky, you will have the first omen really quickly, with only two or three medium difficulty fights you must do. After that, things get more difficult. You may have to do some more fights to avoid one of the situations I mentioned above, perhaps even a hard level fight, or one against more than one enemy. Since you don't want to farm, remember to always choose the "safe" options in quests: the ones that don't bring extra enemies, make them stronger or make you weaker.
If you get two Omens in sequence, it is almost always ok, worst case just use some healing items. Two Omens together is bad but maneageable if you have experience in dealing with them. Gargos coming before all buffs are removed is a "restart the campaign" situation.
Be careful if you decide to give a lesser artifact to a fighter during campaign. You can't remove it before the set number of turns. So plan it right, so as to be able to have the slots free when needed, or only give them the best artifacts from the start.
III - The fights
General strategy for all fights:
With the setup I mentioned, the strategy is a little different for each fighter, but the idea is the same: spam and abuse an attack with which the AI does not deal well.
I used Eyedol mostly for Omen and Gargos, almost never to a normal quest fight. With Eyedol, you want to try to hit a hard attack as soon as possible. After that, you want to simply use the advantage from the guardian and spam grab your enemy until time is over. You just grab, and grab, and grab. If you can do this, you may take around 1/2 of its bar health before you have to hit him again. So wait in defense, trying to block the attacks, until you have the opportunity to counter. Then, hit the enemy with a heavy punch or kick. Eyedol's natural immunity against some hits from Gargos and Omen works like an armour, so even if you time it wrong, you may still not get stunned from getting hit and actually land the heavy attack. After that, get close and spam grab. This is easier said than done, but with practice, it works wonders, specially for Omens.
Riptor was the one I used most for when I had to do normal quest fights, and when I had to fight two Omens in the same turn. With Riptor, you want to use strong punch. The fire attacks makes the AI glitches and it does not respond well. Approach by jumping and using the attack facing down, and spam it as soon as you land. Once it hits, start a combo and try to go as far as you can. Your guardian helps protecting you, so you can hit the first hit and start the combo even if you receive a hit yourself.
Watch out if you look for videos. After the patch, the AI is much better against Riptor, so even if this trick helps a lot, it is not as good or easy to pull off as you may find. Starting a good combo after the hit, and trying to make it diverse so as to not receive a combo breaker were fundamental parts for me, and in some videos I found the player did not need this, it was just a one button spam. The idea is the same, but you need a little more skill for timing it better and continuing the combo.
I used Rash too little, to be honest, in Godlike. The tip here is to spam light punch or light kick, without stopping. It is a fast attack, and it will almost always hit the enemy when it is trying to hit you. The snake guardian can take lots from enemy's health, so if you later manage to hit a combo ender, you will cause quite a good amount of damage. Again, watch out for videos. The AI reacts better against Rash now. Be fast and spam light attacks even faster than you would with Riptor. The enemy will defend, and when it stops defending to try to attack, you will be faster and hit him or her. Then, just start the combo. Sometimes it is good to make it short to avoid combo breakers and use the guardian's ability or cash the potential damage.
One last thing, for a killer start in a fight, specially against Gargos: you know your rotent brain consumable? If you start a fight with full instinct and shadow meter, as soon as you hit the first hit for combo, use it without letting the combo stop. No more combo breakers, and you are in the middle of a combo. Oh, plus extra damage. Use both your shadow meters for shadow attacks, and user your instinct when you are almost filling the combo meter to reset it. All together, you will have a huge combo, both shadow attacks will hit, and you might even have a little instinct left later. With a good execution, which means starting your shadow attacks really early, your shadow meter will also be almost full for one use after you are done.
This is not so hard to pull off, but it is not easy as well: using the item without dropping the combo, and keep an eye to use instinct and shadow attacks correctly, plus not receiving a combo breaker one milisecond before you use the item can be tricky. However, you have three chances to do this. If you manage to pull it off, you take away almost one full health bar from Gargos, no joke. In my winning run, I took a combo breaker the second I used the item with Eyedol, but I was able to pull it with Riptor. This attack was the reason I did not need Rash, I took one full health from Gargos with it before he had barely touched my Riptor.
1 - Omens
I am not a good player, and even so I was able to take Omens down with either Eyedol or Riptor and only using a guardian. So I did not use any consumable or artifact on them, although sometimes the fight was really tight, and two or three times my first fighter died close to the end, and I had to finish with the next one.
In general, you want to try to have at least two fighters, for playing safe.
Omen's AI act almost always the same way: create a lot of orbs, then go for the sliding low kick. If you get away from him, just go as far as you can, and defend while crawling. Wait for the orbs and the low kick. As soon as you defend the low kick, hit and start a combo. If he combo brakes you, go away and repeat. If one orb still hits you, Eyedol does not get stunned and Riptor's armor should take care of it. With Eyedol, you want to hit a heavy attack and start the grabbing spam.
Also, a good variant is trying to jump over the orbs he sent, and hitting him on your way down to start the combo. It is a little more risky, but again the armor and Eyedol's ability should come in handy.
All together, just train against this attack, because he will be using it A LOT.
2 - Gargos
Gargos will have one buff in the fight. If it is the health regeneration buff, you may want to save your items and simply quit. The health regeneration buff is really cheap: in one combo that fully hits you, he can regenerate a good chunk of health back. Some guides recommend you actually try to get the health regeneration buff in the first or second Omen, so you can make sure you won't face it. One thing that I did and it helped is playing in a lower difficult until he gets this buff in the final fight, fight him there (win or lose, it does not matter), and then try Godlike. I did this twice, and both times he got a different final buff than in the previous campaign. Anyway, be advised that this buff makes this fight way harder than it already is, and than any other buff he could have.
Gargos has a few more tricks than the Omens. He is not so easy to fight and he will usually change his patterns. Jumping against him is usually a bad idea, because he has solid anti-air attacks that he will use and abuse, starting huge combos. Approaching him by running is usually better and safer.
He loves to use the attack that he enters the portal and exits above you. Be prepared for it if you stay far away from him. He may also decide to use his portal punch to hit you from a distance. Trying to actually make him comes to you, defending or using your armor to get the hit, and then start hitting him and using the glitches I mentioned is usually the best idea. If you are lucky, he will use the teleport attack, which you can defend and start attacking in the next instant. This is the best attack he can use for you, as it is the easiest to deal with.
He will take the initiative and try to put pressure on you, so be prepared for it. If you can make him come and react correctly to his attacks, you will be able to hit him at least a couple times before he uses a combo breaker. That is the way to go. Be really careful about taking the initiative if you are not putting pressure on him, because he will hit you instead by countering you.
That said, once you have the opportunity, don't let him breath: stay right close to him using the glitch all the time: when he gets up, be right next to him, already spamming the button for the respective character's glitch. Remember Eyedol and Riptor can sometimes take a quick hit and still start a combo. When you get separated, go back to defense like before, hoping he uses the teleport attack or creates an openning, and repeat.
Also, remember to deal with Gargos last life after you put him down the second time. After you defeat him, keep spawning heavy attack over his body!!! Don't stop!!! If you do it, you will hit him and stop his revival with only half a health bar, instead of a full one, plus in the advantage of being already in a combo. If you are lucky, you will leave him to around one quarter health, and next attack will already put him in danger and allows the ultra combo to put him down a third time, this one for good.
Last, be careful with his minions: he loves to spam them, and they can change the course of a battle. The best is to try to not let him have shadow meter by using the item, but if the minions get there, be extra careful. They can hit you from behind and prevent you from actually making any combo at all. Having all enemies in front of you guarantees that you can still spam the glitch button and hit them in the process, so this would be the position to get into if possible.
Well, I think this pretty much covers all aspects, and helps by compiling all the comments and tips from previous guides in one place, plus adding some new content. If you down vote, please let me know why.
Good luck with this achievement!