Is this from Soseki’s 夢十夜?
If so, the original sentence is:
自分は透き徹るほど深く見えるこの黒眼の色沢を眺めて、これでも死ぬのかと思った。
Looks like a tiny difference, but the の between 黒眼 and 色沢 is important, as the particle の indicates the object is the luster (色沢) of the pupil (though, @phyro guessed it right without it! ).
Anyway, not sure what Misa’s method is exactly, but more complicated the sentence is, finding verbs first may not work too well. For example, this sentence has 5 verbs and a couple of them function adjectivally. Identifying the verb that’s the core of the sentence is important, but if you translate all the verbs first, to me personally, it feels like it may confuse Japanese learners.
Anyway, it is not really a method, but if I explain the meaning and the structure of this sentence…
Vocab
自分: I
透き徹る: to be seen through (intransitive verb) = adj. transparent
深く: deep
見える: to look, to seem
黒眼: pupil
色沢: luster
眺める: to stare
死ぬ: to die
思う: to think
If I Break down…
自分は
“I,” the storyteller. This is the subject of the sentence.
透き徹るほど深く見える
___ほど●●● = so ●●● that ___
“so deep that looks transparent”
This chunk describes この黒眼の色沢 which comes next.
この黒眼の色沢を眺めて、
“starting at the luster of this pupil,”
If combined with the previous chunk, it’d be “starting at the luster of this pupil that’s so deep that looks transparent.”
これでも死ぬのかと思った。
“(I) wondered if (she) would really die.”
The subject “I” is at the very beggening of the sentence. It doesn’t include the subject for the verb die, but I identified it was “she” from your translation.
@phyro did a great research on これでも.
If without これでも and it was just 死ぬのかと思った, that’d have been “I thought (she) would die.”
But これでも adds the feeling of doubt. Is she really going to die?
So this indicates that the storyteller isn’t sure if she’s actually going to die. He doubts it because she still has unclouded eyes (which I think implies she’s still healthy).
Not a natural translation, but if all combined,
“I wondered if she would really die, starting at the luster of this pupil that’s so deep that looks transparent.”
I looked up and checked the context. Before this sentence, she was repeatedly saying “I think I am going to die.”
This makes sense as the storyteller doesn’t believe she’s actually dying because of the look of her eyes and what she’s saying is contradictory.
Hope this helps. I never thought of a tactic or a tip for reading, so if I can come up with one, I’ll share here.
But for this instance, you may want to work on vocab, idioms, expressions. That won’t be a waste of your time. Every WaniKani’s vocab has a few context sentences and they aren’t too complicated, so it might be a good starter of your reading practice. 
Also feel free to let me know if you run into something specific that you couldn’t figure out by yourself. I’ll try to help!