Karışımın yoğunluğu arttıkça tadı biraz daha yoğunlaşıyor.

The suffix -dıkça attaches to a verb or adjective stem to mean “as … (happens/changes), …”. It’s a kind of “the more … the more …” construction.

• arttıkça = art- (to increase) + -tıkça → “as it increases”

Turkish uses the genitive + possessive NP construction for “X’s Y”:

• karışımın = “of the mixture” (genitive)
• karışımın yoğunluğu = “the density of the mixture”

In Turkish, definite direct objects take the accusative. Here you’re referring to a specific property, “the taste,” so it’s definite.

• tadı = tat (taste) + -ı (accusative)
  Without –ı (i.e. tatı), it would sound indefinite or general.

yoğunlaşmak is a verb meaning “to become intense/dense” (from yoğun, “intense/dense,” + -laş-, verb-forming suffix).

• yoğunlaşıyor = yoğunlaş-
  • -ıyor (present‐progressive) → “is becoming more intense/dense”

biraz daha literally means “a little more.”

• biraz = “a bit, a little”
• daha = “more”
  Together they soften the increase: “a slightly stronger/more intense flavor.”

Turkish often uses the present‐progressive (-iyor) for habitual or general truths, not just ongoing actions.

• Here it implies “whenever the density increases, the taste keeps getting more intense.”

Yes, you could say:
• Karışımın yoğunluğu arttıkça tadı biraz daha yoğun olur.
This uses -r (simple present) to state a general fact:

• yoğun olur = “becomes/intensifies” in a more static sense, whereas yoğunlaşıyor feels more dynamic. Both are correct; the choice is a stylistic nuance.