It's easier to memorize a pattern than a paradigm. Instead of memorizing the conjugation, you could memorize a rule to identify it. This is more useful when you're trying to understand a text, rather than to be able to express yourself in a language, but ability to express yourself is also better after a lot of exposure to the language, which would make memorization easier.
There are tricks for every conjugation. Niph'al always starts with ni (perfect), or geminates the first letter of the root (imperfect). Pi'el always geminates the second root letter after an i (perfect) or a (imperfect). Pu'al always geminates the second root letter after u. Hiph'il always starts with hi (perfect) or a consonant + a (imperfect). Hoph'al always starts with ho (perfect) or consonant + o (imperfect). Hitpa'el always starts with hit (perfect) or consonant + it/et (imperfect).
If you can remember the previous paragraph, and already know the qal conjugation, you can identify anything on the perfect/imperfect part of the chart. It might not be enough to express yourself perfectly, but is it good enough for reading?
Irregular verbs are also best remembered through patterns. It's probably not a good idea to ignore them in favor of regular tables, since you can't parse Biblical Hebrew well without having at least some knowledge of them. The first two verses of Genesis already have the forms בָּרָא (not *בָּרַא) and הָיְתָה (not *הָיְהָה) and מְרַחֶפֶת (not *מְרַחֶּפֶת). Your chart is also missing the so-called ו-consecutive conjugation (quite similar to the imperfect, but also different enough to pose a problem already at Genesis 1:3).
Recognizing a few things might make this easier:
The names of the conjugations (with the exception of qal) are the same as the 3rd-person masculine perfect conjugation of the root פעל. If you know the names of the conjugations, you already know a whole row from the chart (complicated only slightly since the letter ע can never take a dagesh as it should in the pi'el, pu'al, and hitpa'el conjugations).
The prefixes and suffixes are the same across every conjugation. Since you already know the qal conjugation, you can likely already identify the tense and person of any verb, even if you don't know which conjugation it is in.
If you're looking for irregular verb conjugation, there is a collection of charts here that could be of use.