Fallout 4 on Very Hard Difficulty

Don't do it. Not without mods.

Difficulty in Fallout 4 is basically unrewarding because you don't get more XP for your kills. So these things happen and very quickly the game becomes really grindy-boring:

• If you don't stealth, you die.
• If you don't one-shot things, you will also probably die, unless you can get back your [Hidden] status through stealth. You will basically be sniping just about everything.
• If your build doesn't emphasize stealth, it's no good.
• You are missing out on un-stealthy things like Power Armor and certain encounters where you are meant to just rush in and be the hero. Also, your Companions are idiots and Stealth is hard with them. But at least they are unkillable and can take hits for you, especially if they were the ones that drew aggro on a Missile Launcher using Super Mutant.
• Some encounters are designed to defeat stealth, such as mole-rats bursting out based on proximity, and Radscorpions immediately (literally, immediately no matter the distance) tunneling to your location when you snipe them and your hidden status becomes [Caution].
• You will start avoiding encounters because the cost-benefit is too low. Coming out of a fight with four mongrels with crippled limbs and having to use stimpacks -- all for maybe 4 pieces of mongrel meat? Avoiding fights further reduces your XP gain and your rate of levelling.

You could just grind around low-level areas until your level goes up, but grinding is an MMO mechanic designed to keep everyone playing and feed the pockets of the devs through subscriptions. It has no place in a Single Player game.

If you really want to do Very Hard AND keep the game moving reasonably, you can do two things:

• Have a decent build. Start with at least Agility 7 and Strength 2 (or Strength 1 and use the SPECIAL book to get it to 2) and get the Ninja and Big Leagues perks as soon as possible to help you one-shot as many things as possible.
• They will serve you better than going for Blacksmith or Gun Nut because of the level limitations on the higher ranks coupled with stronger weapons needing higher ranks for the same modifications (such as the all-important Suppressor for a rifle).
• As you level, you will find gear with mods and you can just cannibalize them onto your weapons without making your own with the perks. The perks make it more convenient, but the level requirement is too close to their random appearance on enemies and in stores.
• For stats, I recommend:
• Strength 3 for Big Leagues and to set yourself up for Armorer if you want Ultra-Light armor.
• Delay getting Armorer till you can get rank 3 for Ultra-Light. In the meantime you can strip the Shadowed mod from any armor you come by.
• Shadowed and Ultra-Lights are really quite optional if your Agility is very high and Sneaking related perks maximized whenever you can. Focussing more on damage to one-shot enemies is more important.
• Blacksmith is for the later-game, probably past level 25 -- you really only want it for special Power Armor mods.
• Melee weapon mods aren't easy to find or buy, but the scary bonus from Ninja is so huge you generally don't need it, especially if you pick up General Chao's Revenge early.
• Perception 4 for Locksmith and Rifleman.
• If you don't care to pick locks for the ammo, it's not that big a deal. However picking locks sometimes lets you get a strategically better entry location.
• Charisma 1 but by level 40 you want Charisma 2 and the Lone Wanderer rank 3 perk for a massive +25% damage boost.
• Intelligence 8 for Hacker and Robotics (you will want Robotics for the Automatron DLC but it is probably not necessary prior to that). Gun Nut, Science, and Nuclear Physicist can wait.
• Gun Nut is largely unnecessary for a long time as you can buy or find mods on guns and with Ninja and other damage perks you can generally keep pace with enemies.
• Science is later-game for Power Armor mods. In the early game, Power Armor might be more of a hassle than a benefit.
• Agility 7 for Sneak and Ninja, both of which you need to focus on in tandem with Big Leagues and Rifleman in the early game. Once you've found some Suppressors for your rifles, take Mister Sandman to keep improving your chances of a one-shot-kills with sniping.
• Work toward Agility 9 Blitz if you like, to help you sneak up to melee distance without losing stealth. But honestly the distances you can rush with Blitz are so obscene as to be immersion-breaking. Still, great later on for lining up multi-hits when Big Leagues lets you hit multiple targets.
• Luck 3 for Bloody Mess.
• Work up to 6 later and take Better Criticals, but that has lower priority. A melee Ninja-Sneak using a VATS Critical is probably overkill for trying to one-shot Legendary enemies unless they are beefy ones like Yao Guai or Deathclaws and the like. You'll start not being able to one-shot some bosses and Legendaries in the late level 40's but if you are behind them, VATS melee will often let you get in multiple Sneak attacks to kill them nearly as well as one-shotting them. If you don't, you could get in trouble sometimes, so Better Criticals can come in handy, as can Critical Banker.

You may one to get an XP mod for more kill XP to help you keep up with the enemy difficulty and keep the game moving and not get bogged down in grinding, but once you get gear good enough to one-shot-kill with Sneak Attacks, it'll seem like double-dipping since you can't kill things much faster than one-shotting them.

Under no circumstances should you get a mod that lets you increase Legendary drops (e.g., by increasing Legendary encounters), build Legendary effects, or swap Legendary effects from one piece of gear to another. Legendary items are already balanced by virtue of not showing up often and being tied to a piece of gear. It'll be too easy to assemble overpowered gear sets by around level 30 when you don't even really need them.