#TL;DR - Literally impossible unless the Jinx was braindead and stood still for minimum 4-5 seconds, potentially more.
7.83 Magic Pen from Runes + 4 Magic Pen from Masteries = 11.83 Magic Pen
4.95 AP from Quints x 3=14.85 + 9.7 AP from Masteries = 24.55 AP
6.4 bonus AD from Masteries
40AD, 80AP from Gunblade, the active deals 211+30% AP which is 242.365
24.55+80=104.55 Bonus AP (and Total, since she has no flat AP)
6.4 Bonus AD
155 + 100% Bonus AD + 70%AP = Each dagger deals 155 + 6.4 + 73.185 = 234.585
TLD = 100 + 30% bonus AD + 10% AP = 100 + 13.92 + 10.455 = 112.375 damage.
Her full combo without ultimate: E to target, W for dagger prep, Q enemy, E to W dropped dagger, proc passive, E to Q dropped dagger, proc passive.
Q rank 5, W rank 1, E rank 3, R rank 1 (by level 10).
Q is 195+30% AP=226.365
E is 60+25% AP+50% AD=60+26.1375+(50% of 6.4 bonus + 83.1 flat AD at level 10 + 40 AD from Gunblade)=150.8875
Thus the combo deals 150.8875+226.365+150.8875+234.585+150.8875+234.585 from the combo alone, which adds to 1148.1975. With TLD, it goes to 1272.5725. With Gunblade on top of that, it goes to 1514.9375.
11.83 Magic Pen versus 30 Magic Resist on level 10 Jinx = 18.17 effective magic resist, which is a 0.84623847 multiplier. Katarina thus deals 1281.99839 damage. For it to deal 2000 like the OP said, she must deal another 848.462503 RAW damage for the magic resist to lower it to the necessary 718.00161 to reach 2000 damage dealt.
Katarina's ultimate deals 25+19%AP+22%BAD per dagger, with daggers being thrown every 0.166 seconds (15 daggers total). 25+19.8645+10.208=55.0725 per dagger. 848.462503÷55.0725=15.4062827 daggers. AKA, more daggers than entire 2.5s of channeling. Requires an additional autoattack minimum.
Her ultimate alone takes a solid 2.5s of not doing anything except channeling. The rest of her kit as well as the delay with the drop time for a dagger to fall down to the ground means it would've taken somewhere between 4-5 seconds or more.