Can I Create My Own Boss Battle In Minecraft?

No. You can only increase an entity's health in vanilla using command blocks.

You can however hit them with a resistance potion. Which makes them more resistant to damage. Basically it has the same amount of health but damage is reduced

 /summon Zombie:Name(1)"Boss Zombie"-[id:diamond_sword{inhand(Left)}][id:bow{inhand(Right)}],"SummonTrueMob"[Zombie=Half,Skeleton=Half:zombieHead,skeletonArm2+1{Bass:Raksol},"Rest=[Creeper]"BigSummon=True

I think there is a way to fix this problem.

I've been playing around with boss fights and battles, and at the moment I'm working on a project myself

Here is a command that will summon a zombie that won't burn in the light and it will have 100 health and a diamond sword (Copy and paste this into the chat):

/summon minecraft:zombie ~ ~1 ~ {CanPickUpLoot:0b,Health:100,Attributes:[{Name:"generic.maxHealth",Base:100}],IsBaby:0,HandItems:[{id:"minecraft:diamond_sword",Count:1},{}],ArmorItems:[{},{},{},{id:"minecraft:stone_button",Count:1}]}

I could add more stuff to it like the boss will glow, it will have a custom name at the top of it's head like The Boss!!! and it could have an enchanted sword and when you kill him he drops the sword. I could also add a whole lot more but you would have to use only one command block.

if you don't know how to get a command block then you just do this:

/give@p minecraft:command_block

That will give the nearest player a command block, or if in a single player world or if your the only one in it, it'll give you the command block.