Based on the guide by Czertinski I decided to try some variation on the explody kamigoblin boys and found some interesting combinations.
https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?id=2751113907
Use 2 Kamigoblins and a Goblim Drummer to blow up heroes. Other Monsters or Traps are optional. Getting the artifacts Knight's Ashes, Catapult Seat or Rallying Banner make this extremely easy.

**Update March 28th 2022: Changed the Merchant Event from useless to useful and updated Closing Argument

**Update June 27th 2022: Final update: Updated the Closing Argument with data from my last run.

Before entering Endless Mode we set up the following Talents, Monsters, Traps and Monster types:

The only actual useful talent for these runs is the reduced training price for Monsters. Talents that increase the power and speed of your Master are a good second choice to fill out.



We select 2 Kamigoblins and 2 Goblin drummers. The 2 additional Goblins are optional and just for filling up the roster and can be used for early Business Trips. For traps we need at least the Oil Cauldron and the Circular Saw is again an optional pick to place just in front of the Master's chamber should a party reach it.



I selected Skeletons and Dragons based on personal preference. Since we'll be doing a lot of Fire damage (and Burn), and some Heroes are extremely Fire resistant, you can possibly use some monsters who do Ice damage. Demons don't have many options there.

Before you do anything you can move all your monsters except the 2 Kamigoblins and 1 Goblin Drummer to your Garrison. What we're aiming for from now on is setting up the first monster room so they always go first. The Goblin Drummer (being the fastest) should always Enrage the Kamigoblins and they should blow up the heroes in one go.

• Place the Oil Cauldron in the 1st available trap-room so the heroes Fire resistance drops by 40. (and hope it's before your first monster group).
  
• For the setup of your monster group you can check if heroes do damage to the front- of back-line and what type of damage they do specifically. For now I've just place the Goblin Drummer in the back because I've also got the artifact Miraculous Pill (more about this artifact below).
  
• Place the Circular Saw in the 2nd trap-room.
  
• Skip placing a second monster group.

• I hoped my Goblin Drummer would survive an attack, but unfortunately he didn't because of the artifact. Therefore I just choose to blow up the Kamigoblin(s) with Kamikaze.
  
• For the Master's spell I choose to deal the most damage with the Burning Whip and kill a second hero. Should the fire damage be minimal you can always choose to Enrage the Master via Show no mercy!
  
• The last hero I just kill with the Master trough some Whiplashes.
  
• After killing all the heroes I choose to recruit the Skeleton Executioner, basically because he can do Ice damage and the others can't.

After clearing a run be sure to swap your Goblin Drummer out for a fresh one from your garrison!



I choose the Trainer on the 2nd week to level up one Kamigoblin. This should be your top priority from now on. Get these to level 4 as fast as possible so they get a 75% chance to blow up when they die. Your second priority should be to get your Goblin Drummers to level 4, to give them more speed and extra Enrage. If you want to level up other monsters. Be sure to pull them out of your garrison before choosing the Trainer option.



On the the 3rd week I choose the Business Trip, where I can now use a spare Goblin to get some extra gold. If you can choose the third option, which will always give you some Blood or Tears, without sending one of your Kamigoblins or Goblin Drummers, do it.



For the following weeks you can just rinse and repeat, and be sure to keep swapping your Goblin Drummers.

After your first few weeks and getting your monsters to a minimum of level 4, they should be blowing up heroes left and right. Any heroes that get trough to your Master shouldn't be a problem as well.

You should try to get one of the artifacts to boost the Speed of your monsters as soon as possible. The best artifacts for this are the Catapult Seat and/or Rallying Banner. Therefore the best options to choose in your schedule till you get these artifacts is Business Trip or Event and when fighting heroes be sure to choose the one which rewards you with Artifacts.



After this you can choose the following options to gain some quick Gold based on your available resources:

• Collectors -- always useful for extra Gold if you can spare the Life or Blood.
  
• Siege -- once you get some more traps, this can be a good source for Gold.
  
• Merchant -- once the monsters you can buy via the Merchant get around level 5, you can actually get more Gold buying them here and later selling them via the Black Market.

Around week 500+ Gold didn't seem to be an issue any more and I tend to only go for the following:

• Alchemist -- to transmute any excess Tears to Blood (be sure to keep around 40 Tears for upgrading your Master via Workout)
  
• Black Market -- if you have a lot of monsters you got as rewards from runs or bought from the Merchant. Be sure to keep some monsters around to send on Business Trips.
  
• Business Trip -- the best way to get Blood or Tears on a regular basis via the 3rd option. Just be sure not to send any of your Kamigoblins or Goblin Drummers!
  
• Doctor -- if your Master has lost any health.
  
• Event -- best choice if you're uncertain if the other options are a good idea.
  
• Workout -- if you have a surplus of Tears, be sure to upgrade your Master. Blood should only be used to pump out Power I reckon, because we need it to upgrade our Kamigoblins.

The following options I tend to avoid:

• Course -- the 250 Gold you spend to upgrade a monster is not worth it if you sell the monster on the Black Market later on, and we don't wanna sent off our goblins.
  
• Engineer -- we don't need to improve our traps as we just use them for applying -40 Fire resistance or Bleeding just before engaging. Furthermore if you happen to get the Catapult Seat artifact, traps are no longer needed.
  
• Plunder -- this could be a good situational option for Gold or a Trap Upgrade, but the chance that one of our goblins is out or rotation for a few weeks is a risk we can't take.
  
• Sanctuary -- only useful if you get to Champions in week 300+, but the penalties are still sub par.
  
• Seminar -- same as Sanctuary, but the bonuses are usually not worth it.
  
• Therapist -- as our goblin boys don't lose Motivation, or we can swap them out if needed, we do not need the extra Motivation.

We don't need any additional monsters beside our Kamigoblins and Goblin Drummers, but any additional monsters can be used to send them on Business Trips, sacrifice them in several ways, or just sell them on the Black Market.

For this specific run the Colossal Hydra seems to be the best choice. Any heroes that survive the Kamikaze explosions (due to having high Fire resistance) we can usually sweep up with it's Rock Fall or Venom Spit abilities since they do Physical and Nature damage respectively.



As with Monsters, we do not actually need additional Traps beside our Oil Cauldron and Circular Saw. You can still collect 4 more random Traps and upgrade them as well so we can get some money from if we loan them out for a weeks during a Siege.


Bewitched Glove, "Damage dealt by monsters to heroes at their maximum Life increased by 100%." -- Since our goblins only attack once at before any other damage is done, this is makes the first explosion basically do double damage.


Cheerleader's Pom pom, "You can only place one group of monsters, but their maximum Life is increased by 50% and their Power by 50%." -- Making our first monster group even stronger and making all the other monster available to sell via the Black Market or use on Business Trips.


Horn of Plenty, "Monsters have a 20% chance to deal a critical strike when attacking (+50% damage and Morale)." -- The text says it's only 20% chance, but my feeling says it doesn't work 20% of the time.


Knight's Ashes, "Fire attacks also deal 30% of base damage as Morale." -- This item seems to be bugged at the moment, allowing your Kamigoblins to explode twice. Probably because this causes the monster to flee (which they can't). If you're lucky you can get 4 Kamikaze explosions out of this.


Magic Purse, "Training price of monsters and upgrading price of traps reduced by 30%." -- Should be self-explanatory.


Miraculous Pill, "Monsters placed at the back perform an additional attack but lose 20 Speed and start fights with -50% of their maximum Life." -- If you get this artifact after your goblins always go first, the penalty is negated. This can make the Goblin Drummer use it's War Drum twice, which then gives 10 Enrage (or 100% damage increase), or make a Kamigoblin explode twice.

On my first run I got to week 411 when I met a particularly nasty group of Veterans with both high Armor and Fire Resistance. When they didn't immediately blow up and my Master was having a hard time Whiplashing them, I called it a day.

My last recorded run ended on week 1589 (year 30), because of a bug that I had killing the heroes in the first monster-room and the run not ending. So I decided to let the master finish them, but was just 1 turn short in finishing all the heroes. My Kamigoblins were lvl 64 at that point and if they didn't one-shot the heroes my master could do it with a Whiplash. See the screenshots below.



Good luck with your achievement and be sure to leave a comment on your highest run.