Beleaguered rhymes with:
agard, angered, baumgard, bogard, brungard, bungard, burgard, fingered, haggard, hoggard, huggard, laggard, lingard, lingered, maggard, newgard, niggard, norgard, nygard, odegard, ostergard, sigurd, staggered, sugared, sweigard, thagard, thaggard, triggered, wengerd, westergard, wingard
Beleaguered sounds like:
belcourt, belgard, belgarde, belgrade, blackard, blizard, blizzard