How can one get rid of showing off (riya') and seeking people's approval, and prioritizing that over being mindful of God and seeking His pleasure, and how can sincerity (ikhlas) be achieved?

The desire for people's praise and commendation is something that souls are naturally inclined towards. This is praiseworthy if the person's intent in rejoicing over what they are praised for is that it is a sign of Allah's acceptance of their deed, as stated in the Hadith: "The people of Paradise are those whose ears Allah fills with the good praise of people, while they listen." As for relying solely on people's praise and seeking it, believing it to be a virtue, this is blameworthy and hinders the heart's journey towards Allah. The way to overcome this is by bringing the meanings of Allah's Names and Attributes into the heart, and by realizing that true praise and blame come from Allah alone, for "there is no one whose praise benefits and adorns, or whose blame harms and shames, except Allah alone." This requires patience and certainty, and the stronger a servant's knowledge of their Lord becomes, the more their ambition will be directed towards Him.