I like her too ill to attempt it

As is often the case in classical literature, words and ideas are being juxtaposed in ways in which you wouldn't usually expect to find them for poetic effect.

What does 'And I like her too ill to attempt it' mean?

You need to break the sentence down and separate the parts you do understand from the parts you do not.

And (superfluous) we can ignore it (I assume you know what and means)...

'to attempt it' - I assume you know what this means? or can readily find the answer in a dictionary... It's connecting to the earlier part of the passage (to...absolutely seize and devour her up).

Which leaves us with what exactly? The less ordinarily phrased

"like her too ill"

Ill is being used to modify the verb, like so is acting as an adverb here:-

(OLD)

Ill

adverb

... Badly, wrongly, or imperfectly.

‘the street is dominated by ill-lit shops’ ‘it ill becomes one so beautiful to be gloomy’

To like ill means therefore to like imperfectly, badly, or wrongly. In the context of the surrounding passage, you could translate I like her too ill into modern English by simply stating:

"I do not like her".

or

"I like her in a way that is perverse".

(Depending on your reading).

How do we know what the context of the passage is? That brings us to the second part of your question:

What does the phrase 'turning the blue eyes black' imply?

When you are confronted with phrases you do not understand, try to think about them and ponder how you might use the language presented to connect with ideas you are familiar with.

"turning the blue eyes black"

What does it mean to have your eye turned black? A black eye?...

(OLD)

An area of bruised skin around the eye resulting from a blow. ‘he had fouled three players, giving one of them a black eye'

So piecing this together Heathcliff is describing how he does not like his wife and wishes to bruise her eyes. This interpretation is further supported by the most horrible phrase: "would be painting on its white the colors of the rainbow".

The rainbow vividly painting the idea of bloody reds; against blue,violet, yellow and purple bruising in our imagination.

A very powerful and sickening passage, all the more so for the poetic thought Heathcliffe has given the fantasy of physically abusing his wife.

It means that he is using restraint, in this instance. It's a direct juxtaposition to "I like her too well," where the primary speaker is expressing true affection and a desire to protect Catherine. Heathcliff is then expressing his distaste for Catherine, playing on the previous words by replacing "well" with "ill," and explaining that he would abuse her if they were living together.

To "paint her blue eyes black," is a literary description. Brontë, via Heathcliff, is painting a picture of bruised eyes. Catherine's eyes are blue but Heathcliff would like to blacken them (commit violence).