Much debate has been around the misapplication of metrics in research assessment. As a result of this concern, the Declaration on Research Assessment (DORA) was launched, an initiative that caused opposing viewpoints. However, the discussion topics about DORA have not been formally identified, especially in participatory environments outside the scholarly communication process, such as social networks. This paper contributes to that end by analyzing 20,717 DORA-related tweets published from 2015 to 2022. The results show an increasing volume of tweets, mainly promotional and informative, but with limited participation of users, either commenting or engaging with the tweets, generating a scarcely polarized conversation driven primarily by a few DORA promoters. While a varied list of discussion topics is found (especially "Open science and research assessment," "Academics career assessment & innovation," and "Journal Impact Factor"), the DORA debate appears as part of broader conversations (research evaluation, open science). Further studies are needed to check whether these results are restricted to Twitter or reveal more general patterns. The findings might interest the different evaluators and evaluated agents regarding their interests and concerns around the reforms in the research evaluation.