He entered the negotiations putting on a bold front.
虚勢 means a false show of strength or bravado, while 虚栄心 is the underlying desire for admiration, not a performance of toughness.
虚勢 means a bluff or false show of strength/courage, whereas 虚栄 means vanity about one's appearance or achievements; the two are easily confused because of their shared 虚 and similar sound.
Compound of 虚 (false, empty) and 勢 (power, force). The exact historical derivation is uncertain, but the meaning is transparent from its components.