Firstly I wouldn't attempt this until you're at least Level 6 with
Lizzie Pilot for the Buzzkill. The Cryo cannon will take far too long. Do speed-runs of the Clock on Inconceivable to get to level 6 fast, obviously the higher level you are the more cards you'll have you should definitely equip rear armour and stim card due to the pilot's passive more on this below.
Now for the actual solution, load wave 11 on beginner on any map preferably somewhere open, I was using AllFathers Arena but it's a bit too cluttered honestly. When you spawn you'll have a full ultimate and a fair amount of cash to buy the perk that reduces the cooldown time of your ultimate, press
then right on the D-Pad until you've spent all your money on the perk.
To speed this up even further
have a partner join you and get kills on enemies you have marked as that's what cools Lizzie's ultimate faster. this has now been changed to the default tank passive (when I posted the solution it was still for marking enemies) of taking damage to recharge the ultimate faster as such to speed it up stand in the open and get damaged until you've got a bright red omen then take cover to regenerate your health OR take damage to die and just respawn as that adds to your ultimate no need for a friend/second player to speed it up.
Then it's simply up to you to get kills with your silverback and waiting for it to cooldown, quitting and reloading would take longer in my opinion.