I can comfortably kill eclipse & EOS every time without fail relatively quickly, and the trick is to have the Flakker with tediore grip so you get 12 rounds. If you don’t have that, try to go for a purple ravager with tediore grip so that you get 8 rounds with the skill that buffs your mag size.
For flakker, you fire off two shots, and then reload. Repeat as necessary, and getting your health low will dramatically help with DPS. The reason you don’t want to fire off the last shot in flakker is that the 2nd last shot in Flakker gets MASSIVE boost from One Last Thing and so you want to spam the 2nd last shot as much as possible for both Eclipse and EOS.
If you don’t have flakker, Ravager will work as well, although not as quickly. For ravager, you want to empty out your mag (2 shot), reload, repeat as necessary.
It’s a good idea to boost your explosive damage before firing either flakker or ravager by reloading some fast-firing weapon repeatedly, such as any tediore weapons.
Another weapon that works really well is the Mongol.
So TL:DR for destroying Eclipse & EOS as Clappy: get 11/5 in one last thing, boost your explosive damage by reloading a bunch, spam your 2nd last shot in your flakker as much as possible, get your health low, spam last shot in your mongol, and if you don’t have flakker, spam the f*** out of ravager.