I am not sure what's Tehunseen's strategy to solo H4 but I can share with you with mine.
I am healing Operative, I use Temple as companion with AoE abilities turned off.
So up to the last chamber it's quite easy to solo the problem comes when 3 strong mobs and one elite spawn.
I put Kolto Probes on myself and companion before pushing the button. After pushing it there is a brief pause before the mobs are spawned so precast orbital bombardment, also allows you to start Stim boost.
Assign Temple on some strong mob, pop Evasion and Shield and help with dps. By the time the shields ends the 1st mob should be dead. All mobs should be hammering you.
Assign Temple on another strong mob and throw flashbang. Immediately after it damage the focused mob so Temple will continue dpsing him. You will be probably quite low on health by this time but don't fall back to healing yourself yet. Debilitate -> Eviscerate -> Backstab the focused mob and start healing yourself. The focused mob should be almost dead when other enemies kick back into fight. Now is the time for Endorphin rush, Medpacks and other healing CDs. When the 2 strong mobs are dead it should be easy to heal yourself.
Be careful to not let Ensign take the aggro through fight. There isn't much time/health for taking aggro back or healing 2 targets.
After this pack pull back a bit behind corner so the ads will come approximately into same spot. Turn AoE abilities of companion ON and select Assault mode (AoE). The ads can be basically AoEd like this. Dps only with Frag grenades, Orbital strikes and finish almost death enemies. It's not that hard.
The final boss is even more simple to solo
And yes I like to solo difficult heroic missions too