You can't; you want força fantasmagórica

Reacting to the gullible creature

As you've noted, any physical interaction with the image (fighting it) would result in learning that it's an illusion. It doesn't matter how gullible they are, they're interacting with it so it's going to become an illusion.

Major image is also somewhat explicit in how you can use your action to 'move' it and what you can do with the audible portions of the illusion:

As long as you are within range of the illusion, you can use your action to cause the image to move to any other spot within range. As the image changes location, you can alter its appearance so that its movements appear natural for the image. For example, if you create an image of a creature and move it, you can alter the image so that it appears to be walking. Similarly, you can cause the illusion to make different sounds at different times, even making it carry on a conversation, for example.

Given that you have to use your action and this isn't a preprogrammed 'conversation', there is no way you can make it respond to a creature's attacks.

If the gullible creature attacks it, it has no AC and there is no hit/miss. It just becomes the physical interaction with the illusion which results in discovering it's an illusion.

Embed the illusion in their mind

What you need to do is use a spell that convinces the target that it's real. I'd recommend the following:

Força Fantasma - 2nd level

While a target is affected by the spell, the target treats the phantasm as if it were real. The target rationalizes any illogical outcomes from interacting with the phantasm. For example, a target attempting to walk across a phantasmal bridge that spans a chasm falls once it steps onto the bridge. If the target survives the fall, it still believes that the bridge exists and comes up with some other explanation for its fall - it was pushed, it slipped, or a strong wind might have knocked it off.

A gullible target still has an opportunity to use an Investigation ability check, but if they're gullible, then a DM could rule that they'll just keep fighting the creature thinking it's real and never require the ability check.

Other won't see what they're fighting, but the target won't care. They'll keep on keepin' on and fight the good fight against the illusory creature.

A Readied Action Would Enable the Illusion to 'Dodge'

As the Major Image spell allows the caster to use an action to move the illusion, they can use a readied action to have the illusion move ('dodge'). The caster would need to declare a readied action such as "I will move the illusion when the fighter begins their attack". Any declaration that would allow the reaction to occur before the attack connects would be sufficient.

As the illusion moves away before the attack hits there is no interaction. Though the illusion would need to move just far enough that the Fighter NPC can't use the remainder of their movement to reach it for another attack. As a 10th level Fighter (or 1st level two-weapon fighter) would have multiple attacks, after using the readied action the illusion needs to be safe from interaction (the other attacks) until you can ready another action for the illusion to move ('dodge').

Though since the party is running away the caster would need a way to observe the battle to use the readied action. Which can be done with a Pact of the Chain Warlock with the Eldritch Invocation; 'Voice of the Chain Master'. This would allow the caster of the spell to observe the battle (through their familiar's senses) and use their readied action to move the illusion upon seeing the trigger.

• Major Image PHB 258
• Readying an action PHB 193
• Voice of the Chain Master PHB 111

TL;DR - Major image explicitly states that the only control you have over the illusion is to make it move from one spot to another or emit sound, which it will do in a natural fashion. Dodging attacks thus doesn't seem to be within the possibilities of this spell. On the other hand, Project Image and Mislead both allow you to make the illusion "behave in whatever way you choose", which should include more complex actions such as dodging attacks.

Rules as written, it seems that what you seek to do is impossible to perform using Major Image. Simply put, the Investigation check is for observers not physically interacting with the illusion, and the NPC would immediately notice something is wrong when his blade goes through the "monk". From the spell's description, the only actions explicitly allowed for the illusion are moving from one place to another within range and emitting sounds, which the illusion will appear to do in a natural fashion. Complex actions such as evasive maneuvers are not explicitly mentioned in the spell's description, and can't be replicated by simply moving the illusion around, at least not realistically.

Personally, I'd rule that such fine control of the illusory monk isn't possible with major image, especially as you control the illusion from an outside perspective. For an example of how difficult this can actually be, you can watch this video of people playing soccer/football using VR glasses to see from above instead of with their eyes. Note that these soccer/football players are also directly controlling their own bodies rather than mentally ordering an illusory clone around, which intuitively feels like it would be more difficult.

Spells that should have the desired effect.

Imagem do Projeto (PHB p.270) is a 7th level illusion spell accessible to wizards and bards which allows them to project an illusory clone of themselves up to 500 miles away. As with major image, the illusion is intangible, and it actually dissipates if it takes any damage. However, unlike major image, the spell allows you to "ride" the illusion, spending a bonus action to see through the illusion's senses.

You can use your action to move this illusion up to twice your speed, and make it gesture, speak, and behave in whatever way you choose. It mimics your mannerisms perfectly.

This could be interpreted as the illusion mimics your actual movements, or at least performs the commanded action like you would have performed it. So you could mentally command it to "dodge", and it would dodge to the best of your own abilities. Failing that, you could argue that your physical body performs the dodge and that the illusion mimics your movements.

All of this is moot if your DM allows you to actually act through the illusion while you share its senses, however (as a 7th level spell, it deveria be cool and powerful). Nonetheless, the possibility to have the illusion "behave in whatever way you choose" implies that dodging attacks should be possible, unlike major image.

As a DM, I'd rule that if the attack would've missed your character (counting only your dexterity modifier to AC, as a hit to the armor would technically go through the illusion and thus reveal it as such), then it also missed the illusion, provided you are currently sharing its senses and actively trying to avoid the attacks. Think "Luke Skywalker vs Kylo Ren", except that you can't afford to get hit.

If your DM is generous, Enganar (PHB p.260) would provide another alternative. As a 5th level spell, it is more easily accessible to the players. Like project image, it allows you to make the illusion "behave in whatever way you choose". But unlike Project Image, the spell description does not actually state that the illusion mimics your mannerism, despite the fact that you can still share its senses to control it. If your DM requires that, only project image would qualify. On the plus side, it doesn't dissipate if it takes damage, but most DMs would likely rule that it would still reveal it as an illusion.

Getting the monk to cast these spells.

The problem with those two spells, however, is that although they seem to be just what you need, they can only project an image of the caster. As such, you'd need a way to have the monk cast it himself if you want your original plan to work.

A anel de armazenamento de feitiços (DMG p.193) allows a spellcaster to store up to 5 levels of spells in a ring, which anyone can then attune (no spellcasting requirement) to cast the spells stored within as if they were the original caster. While this wouldn't work with Project Image (7th level spell), it does work with mislead (5th level spell), provided that your DM accepts that Mislead functions the way you want it to function.

A rolagem ortográfica (DMG p.200) would also allow the monk to cast the spell, as long as you can find a way to get Project Image on their spell list. A single level dip in the wizard or bard class, though not exactly efficient for most monks, would work just fine, provided that they can succeed an Intelligence or Charisma check (DC17 or DC15) when casting the spell. To reduce the chances of failure, cast guidance and enhance ability on the monk before he attempts to read the scroll, so he gets a 1d4 bonus on the roll as well as advantage.

Finalmente, poções exist for other illusion spells such as Invisibility. If your DM allows you to brew your own potions, the party's wizard could create a potion of Mislead or a potion of Project Image, which the monk could then drink at the appropriate moment. The process for creating such a potion would be up to your DM, but it would technically be possible.

Conclusão.

In the end, the hardest part of this plan (other than convincing your DM that these spells function the way you want them to) is to find a way to have the monk cast the required spells. If you can manage it, however, I would definitely allow it as a DM, even allowing the monk to add his wisdom modifier to his AC when "riding" the illusion, as he's technically sharing its senses and reacting as if he were there.

Were I your DM, I'd definitely allow project image to work as you plan it to, but probably not mislead, as it does not specify that the spell mimics your mannerism perfectly.