赢得 emphasizes what was won or gained. 赢 alone means simply 'to win'. 赢得 takes an object: 赢得比赛 (win a match), 赢得尊重 (earn respect), 赢得支持 (gain support).
memory
赢 is one of the most complex common characters to write (17 strokes). Memory trick: it contains 亡 (death), 口 (mouth), 月 (moon), 贝 (money), 凡 (ordinary) - to win you need everything.
