If you fire it from point blank, it minimizes the enemy's time to respond. I've popped many a target this way. Another thing you can try is launching it with a cluster of other pets, such as mines, boarding parties, scorpions, MVAM sections, and anything else to increase the amount of targets the enemy has to deal with.(although with the new TS and FAW, this doesn't work as well)
In PvE, it seems the NPCs are only shooting at Tri-Cobalts if you haven't inflicted enough damage (basically creating "aggro") against them. So if you fire a few beams or cannons at each of them, you should have their full attention.
It seems, though, that Tri-Cobalts can sometimes also be intercepted by torpedoes, or at least that is my impression. That might be more difficult to deal with.
Against enemies with Beam Fire At Will, you will have to wait for that power to run out.
In general, of course, it's best to use the Tri-Cobalt at very close range. You can for example use Evasive Maneuvers to get into close range, fire the Tri-Cobalt and then turn 180° to keep firing on that firearc (time this well, otherwise you spend too much time turning or getting distance again.)
Another approach can be to stun the enemy with Photonic Shockwave. That is an option only the MVAM Advanced Escort, Science Vessels, Carriers and Bird of Preys can take (it is a Lt.Cmdr Science power), and it can be a little counter productive, since Tri-Cobalts also provide a stun effect, and this effect will now be wasted - but the damage, on the other hand, will not be.
Don't fire tricobalts while the enemy is under the effect of Jam Sensors or similar effect. Jam Sensors hides you from the enemy's targeting sensors, but anything you fire at them will be seen. And since HY Plasma Torpedoes and Tircobalts can be shot down...
At higher tiers of escort you can almost afford to mount a tric in a forward launching position along with a regular torpedo and the rest of your conventional weapons.
This lets you hit the enemy very hard with conventional beams or cannons + any shield drain abilities you have + conventional torpedoes; then you close to point blank and deliver the kill-shot with the tric.
I haven't tried it yet but I intend to experiment with it.