Soloing in places such as Inferno is tricky if you're not accustomed to precision bot micromanagement, the fine art of pulling exact mobs and the even finer art of avoiding others' trains. On RK come TL7 unless you've just run into a stack of 30 GUPHs (

) there's little that should faze you. AI ground raids and the gens can be soloed easily, even the high HP/hard hitters if you can juggle agg effectively.
Out in SL though, well, please bear in mind that engis aren't really an endgame soloing profession, sad to say. They
can do it more or less, it just takes a lot of work and practise. Don't expect to solo Zods any time soon and expect a bad inf dyna pull to leave you standing around the garden going 'wtf?'. If you're looking for an easy end-game soloer, roll an Advy
It comes down to how well you can 'tank' damage by juggling aggro between yourself and your two pets. Healing is limited, even with the heal perks, trimmer(s) and nanos. It's important to be able to take a bot out of a fight and let it's own HD regen it now and then, and to be able to shift the agg off of it to yourself and the other pet. If you've gone for a high HP route, you can let the mob(s) whittle away at you for a while until your bot is back up to scratch on the HP front. Blind aura + maxed evades even for an engi can also help out, both with shifting the agg to you and to reduce the incoming damage. Whilst you can BR the bots, it's best saved as an absolute emergency. If you keep backup shells you can toss out in an instant, then spam the critical buffs, then in a particularly hard fight (say vs an inf dyna) you'd want to hold back the BR for when you yourself will end up tanking for a bit for bot recovery/buffing a new bot.
Usually the Slayer would be the tank (and trimming tricks on the dog can help keep it that way) but the higher the SL slayer, the
lower its HP - it's important to keep this in mind. Going full def and switching to a more defense-oriented gear layout can really help as well, both in terms of not drawing agg into yourself unless you really want to - agg management is the key here - and with keeping yourself alive.
At least the new zombiedog has more HP than the old one which means it can tank a little (and with the amount of taunt it generates, even untrimmed it'll grab agg off your slayer/chicken more than you'd like).