During that period the retro look was in — everyone was wearing bell-bottoms.
Tips
usage
阵子 (zhènzi, 'a stretch / a while') is colloquial; 那阵子 specifically points back to a remembered span. Compare 这阵子 (zhèzhènzi, 'lately, these days') and 一阵子 (yīzhènzi, 'a while').
register
Conversational. In writing, prefer 那段时间 (nà duàn shíjiān, 'that period of time') or 那段日子 (nà duàn rìzi, 'those days').