It's gonna be tough for sure, but I think you'll be okay. Laser spam is one of the quicker ways to win though the BL3 is not the best way to do laser spam. Your best bet is to, when the BL3 is about 8 seconds from being fully charged, fire the ion. If it hits, great. Fire everything at their shields. If it misses, wait and fire another ion and then go all out once it hits OR misses. You want to go for shields so they hopefully go down to 2, that way you can follow it up with an ion to take them down to 1 and then a BL2 shot to take them fully out. Then you just shoot shoot shoot to victory.
You can try to take the missiles out or the cloak, but I say just go for the shields and hope they don't shoot anything important. This is not about finesse. It's about killing them as quickly as possible before they kill you.
I'd be a lot more confident in your chances if you had a 4th shield, full engines, a cloak, or defense drones. Or even better all 4 of those things
NOTE: The BL3 and the cloak are on similar timings. With your auto reloader an fully leveled guy, you'll be able to fire it before the 2nd cloak but only just. If you have to wait for that ion to hit, you may be better off waiting through the 2nd cloak. Nothing is worse than having the enemy cloak right as you've unloaded all your barrels.