Scala way to program bunch of if's

It might be nicer to write it as a fold:

def balance(chars: List[Char]): Boolean = chars.foldLeft(0){
  case (0, ')') => return false
  case (x, ')') => x - 1
  case (x, '(') => x + 1
  case (x, _  ) => x
} == 0

I don't think there is any reason to filter the list before you traverse it. You can just ignore the non parentheses as you traverse the list. I think it is also unnecessary to build the second list. All you really want to know is that the count of open parenthesis is never negative:

def balance(chars: List[Char]): Boolean = {
  @tailrec
  def _balance(chars: List[Char], count: Int) : Boolean = 
    chars match {
        case Nil => count == 0   // end of the string did we close every open?
        case '(' :: xs => _balance(xs, count+1)  
        case ')' :: xs => (count > 0) && _balance(xs, count-1) 
        case _ => _balance(chars.tail, count) // uninteresting char, skip it
    }

  _balance(chars, 0)
}

Well:

1. You could start by writing it with else if conditions.
2. Go ahead an annotate it with tailrec since it's tail-recursive.
3. The filter condition can be written more simply as Set('(', ')'), which is a function from Char to Boolean
4. I think you're missing the condition where chars is empty but parenthesis is not.

So it would look like:

def balance(chars: List[Char]): Boolean = {
  @tailrec
  def checkParentesys(chars: List[Char], parentesis: List[Char]): Boolean =
    if (chars.isEmpty && parentesis.isEmpty)
      true
    else if (chars.head == '(')
      checkParentesys(chars.tail, '(' :: parentesis)
    else if (chars.isEmpty || parentesis.isEmpty)
      false
    else
      checkParentesys(chars.tail, parentesis.tail)

  checkParentesys(chars.filter(Set('(', ')')), List())
}

You could also just turn the whole thing into a pattern match:

def balance(chars: List[Char]): Boolean = {
  @tailrec
  def checkParentesys(chars: List[Char], parentesis: List[Char]): Boolean =
    (chars, parentesis) match {
      case (Nil, Nil) => true
      case ('(' :: charsTail, _) => checkParentesys(charsTail, '(' :: parentesis)
      case (Nil, _) => false
      case (_, Nil) => false
      case (')' :: charsTail, '(' :: parentesisTail) => checkParentesys(charsTail, parentesisTail)
    }
  checkParentesys(chars.filter(Set('(', ')')), List())
}