Gears 5

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.

Honestly..

The best grind map for horde is forge.

Play on beginner.

Use the silverback right away and get kills.

And then for next round go press the flame thrower button up top when there is an enemy in the ring. If you get one kill your special fills up again.

Rinse and repeat

It was the best method by far

If, like me, you are getting frustrated by the amount of time it takes to recharge your special ability, I noticed that if you purposely let a Sire grab you, the period that it has you in it's clutches inflicts massive amounts of damage over time without having to recharge your health since you can't go down or be killed in this animation.

Once you locate a Sire enemy, as long as you fail that wave it will always be there every time you restart that wave.

I'd just pop the SIlverback, kill as many enemies as possible, and when it runs out, let the Sire grab me and by the time it kills me and I restart the wave, my ability was recharged.