die Beachtung
attention
The attention or interest that someone or something receives.
Seine Entdeckung fand in der Fachwelt große Beachtung.
His discovery attracted great attention in the professional community.

attention / observance
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attention
The attention or interest that someone or something receives.
Seine Entdeckung fand in der Fachwelt große Beachtung.
His discovery attracted great attention in the professional community.

'Beachtung' (attention / observance) is the noun related to the verb 'beachten' (to pay attention to / to observe). The verb 'beachten' means to give something attention or to follow a rule. The noun describes the result or act of doing this.
Bitte beachten Sie die geänderten Öffnungszeiten.
Please note the changed opening hours.
The meaning of 'Beachtung' (attention / observance) depends strongly on the context. In connection with opinions, media, or science, it means 'Aufmerksamkeit' (attention). In the context of rules, laws, and regulations, it means 'Einhaltung' (observance / compliance).
Sein neuer Film fand weltweit Beachtung.
His new film attracted worldwide attention.
In the meaning 'Aufmerksamkeit' (attention), 'Beachtung' is often combined with the verbs 'finden' (to find / to receive) and 'schenken' (to give). You can give someone or something attention, or something can receive attention.
Ihre Arbeit hat in der Forschung große Beachtung gefunden.
Her work has attracted great attention in research.
In the meaning 'Einhaltung' (observance / compliance), 'Beachtung' is often used in formal or official texts. A typical construction is with the genitive or 'von' to say what must be observed.
Die Prüfung muss unter Beachtung der offiziellen Richtlinien erfolgen.
The inspection must be carried out in observance of the official guidelines.
The phrase 'jemandem/etwas keine Beachtung schenken' (to pay no attention to someone/something) means to deliberately ignore someone or something. The person or thing being ignored is in the dative.
Sie hat seinen unhöflichen Kommentaren keine Beachtung geschenkt.
She paid no attention to his rude comments.
interest
'das Interesse' and 'die Beachtung' both have to do with attention. 'Interesse' more often describes what a person feels internally: they are curious or want to know more about something. 'Beachtung' more often describes that someone or something receives attention, or does not receive it. You can pay attention to something, even without having a strong personal interest in it. 'Interesse' fits more naturally when it is about curiosity or personal engagement. 'Beachtung' fits when something is noticed, taken into account, or ignored.

Im Zug schenkte niemand der lauten Durchsage besondere Beachtung.
On the train, no one paid any special attention to the loud announcement.
Wir zeigen großes Interesse an neuen Lösungen für den Verkehr.
We are showing great interest in new solutions for transportation.