The downfall of Pharaoh and the entire nation of Egypt is a scene of absolute, humiliating destruction, where the bodies of the fallen are scattered everywhere, from the highest mountain peaks to the deepest valleys. The threat of flesh left upon the mountains is not directed at Pharaoh alone, but encompasses the bodies of his entire army and people [רד״ק]. There are different ways these casualties end up at such high altitudes. The Egyptians might flee to the mountains seeking shelter, only to be killed there [רד״ק]. Alternatively, wild beasts and birds of prey will drag the corpses up to the peaks to consume them [רד״ק, מצודת דוד, מלבי״ם].
Down below, the deep valleys will also be filled [מצודת ציון]. The exact nature of what fills these depths highlights different angles of Egypt's defeat and shame. The primary approach among commentators is that this refers to the nation's shattered pride and arrogance. Egypt was a boastful empire that considered itself the representative of the civilized world, taking immense pride in its massive armies [רד״ק, ביאור שטיינזלץ]. Now, all of that arrogance will crash down into the valleys, leaving Pharaoh as a defeated, humiliated corpse stripped of all his former glory [מצודת דוד, מצודת ציון].
Other interpretations focus on the physical horror of the aftermath. The deep ravines might be filled with so many dead soldiers that the piles of bodies will literally rise high out of the valleys [רד״ק]. Another perspective suggests a mass discarding, where countless corpses are simply thrown down into the depths [רש״י]. A completely different approach envisions a scene of severe decay, where the valleys will be entirely filled with the worms breeding within the multitude of rotting bodies left behind [רש״י, מלבי״ם].