From SN 55.5:
“Sir, the factors of stream-entry are associating with good people, listening to the true teaching, proper attention, and practicing in line with the teaching.”
“Sappurisasaṃsevo hi, bhante, sotāpattiyaṅgaṃ, saddhammassavanaṃ sotāpattiyaṅgaṃ, yonisomanasikāro sotāpattiyaṅgaṃ, dhammānudhammappaṭipatti sotāpattiyaṅgan”ti.
According to the sutta above, proper attention (yonisomanasikāra) is required for stream entry.
It's not possible to achieve proper attention, when one is afflicted with the five hindrances. In order to significantly overcome the five hindrances, one needs to have mastered at least mastered the first jhana. You can find more info in this question.
To quote Ven. Dhammavuddho from that question:
The third condition, this word - yoniso manasikara, which I translate as focused attention. Sometimes they say careful attention. This word means that when you listen to the Dhamma, you are focused on listening to the Dhamma. In other words, at that time, you don't have the five hindrances. If that is so, then you can understand the Dhamma and attain stream entry.
So who are the people who do not have the five hindrances? In the suttas, it is stated by the Buddha that as long as a person has not attained piti and sukha which are secluded from unwholesome states, which are secluded from sensual pleasures, the five hindrances will obsess him and obsess him habitually.
... When a person has attained the first jhana, he has eliminated the five hindrances and the Buddha says that the five hindrances no longer obsess that person habitually.
So there are two conditions if a person has the hindrances. Firstly, it obsesses your mind, it enslaves your mind. Secondly, it is habitual, it is very often there. ... When a person attains the first jhana, these hindrances reduce to a very low level. ...
In that question, Ven. Dhammavuddho claimed that instead of the first jhana, it is also possible that persons of high IQ can also achieve proper attention, although this is his personal opinion.
From this page on Nirodha Samapatti:
According to Vis.M. XXIII, the entering into this state takes place in the following way: by means of mental tranquillity (samatha) and insight (vipassanā) one has to pass through all the 8 absorptions one after the other up to the sphere of neither-perception-nor-non-perception and then one has to bring this state to an end. If, namely, according to the Vis.M., the disciple (Anāgāmī or Arahat) passes through the absorption merely by means of tranquillity, i.e. concentration, he will only attain the sphere of neither-perception-nor-non-perception, and then come to a standstill; if, on the other hand, he proceeds only with insight, he will reach the fruition (phala) of Anāgāmī or Arahantship. He, however, who by means of both faculties has risen from absorption to absorption and, having made the necessary preparations, brings the sphere of neither-perception-nor-non-perception to an end, such a one reaches the state of extinction.
So, according to the Visuddhimagga, the 8 jhanas and Nirodha Samapatti isare not absolutely required for attainment of the fruition of anagami and arahat.