Beast radical on the left - the side-form of 犬 (dog). Marks 猛 as belonging to the wild-animal family: the original sense was a fierce hunting hound, from which came 'fierce, violent, sudden.' Same radical in 狗, 狼, 狮, 猫, 獾 - predator and pet alike.
Right side 孟 carries the sound: mèng → měng with regular tone shift. 孟 (a child 子 in a vessel 皿) originally meant the eldest of siblings - the fierce/foremost one. That semantic flavour leaks into 猛 'fierce, foremost in force,' so the phonetic doubles as a faint meaning hint.
