Hi!

About the game

I'm working on top-down 2D hack and slash game, similar to old Zelda style and Binding of Issac.
Our gameplay is in rooms where we have puzzles to solve, enemies and bosses to kill.
Currently, we have one default weapon, dash, throwing projectiles (like shuriken) and other minor features like parry, deflect, pushing objects.

We have played, tested, searched other games to seek what would be the best fit for our game, but we are still struggling with an upgrade system.
Gameplay is simple, you start in one room, advance by killing enemies, destroying (optional) props (chairs, tables, boxes), solving puzzles and killing the boss.

Our thinking
However, we still seek the best way to reward player. Should enemies once they are dead drop some points that are used for upgrades? or fill our ultimate bar? or something else?
Things that could be in the upgrade system are

• Player attributes - better speed / lower cooldown on dash / higher health
• Weapons  (new weapon)
• Weapon attributes - dealing % higher damage, higher range, etc

Hollow Knight is game which does it in a special way where you have badges that you put in limited slots. 
In our game, if bosses drop badges, it would be easy to use (just slot a badge) and players will have a choice to choose their playstyle by choosing badges because there are only a few spots.

Another option would be classical gaining skill points by defeating the bosses, that can be invested in skills/upgrades where we would have upgrade tree. 

However, I'm not sure how different weapon would fit, would you rather like that weapons can be found in some special chest rooms? Or also by defeating a boss or some other way?

Please, feel free to write your opinion and what you like (or don't like) in similar games.
Below are few screenshots from the first prototype of the game.

Maybe something like the item skill tree from Rogue Galaxy would fit your game. It was a two part system, where you crafted Items and used them to gain skills.

In your game you can keep things simple:

Make that each enemy can drop 1 of 3 random items. The player then has to target the right enemies to gain the skills they want.

2 hours ago, markoal said:

However, I'm not sure how different weapon would fit, would you rather like that weapons can be found in some special chest rooms? Or also by defeating a boss or some other way?

Finding loot from chests and enemies only work if you have a large range of weapons. Castle Crushers had limited amount of weapons so finding them became part of the game play.

It really depends on how many weapons you have for the game.

On 6-2-2018 at 1:33 PM, markoal said:

Our thinking
However, we still seek the best way to reward player. Should enemies once they are dead drop some points that are used for upgrades? or fill our ultimate bar? or something else?
Things that could be in the upgrade system are

It's not clear whether you're asking for an upgrade-system, advice on whether to implement an upgrade-sytem or actually talking about a reward system, anyway:

There are roughly three categories of rewards to be found in the levels of a game:

1) Upgrades, weapons etc. (What these would be depends on your game)

2) Health, mana, refill, save-points, generally also ammo goes here.

3) Score, meaningless in-game, yet can be made interesting with collectibles etc.

There's honestly a lot of different ways you could handle this. If anything, prototype type each of them and see which one you feel works best within the game.

And don't be afraid to do small demos and give them to people to ask their opinions too.