You will need to have completed the Botz Only BONUS: 0XDEADBEEF QUEST PT. 1 to unlock Weaver's Test BONUS: 0XDEADBEEF QUEST PT. 2. Once you beat Weaver in the last event in PT. 2, you will unlock the Shockwave (another hydrojet) and this achievement.
I would suggest using either the Scorpion (not available until you finish the main storyline) or the Fireball to beat Weaver. If you cannot beat Krex with the Fireball, you can unlock the Shockwave with a maxed out Fireball (or at least 4 upgrades in each stat).
Weaver was easier than Krex, so you should have no problem unlocking her. Just make sure to use the ramps on lap 3 to give you the extra boost to pull out ahead.