The destroyer is an unloved beast in Eve online. Intended mainly as an anti-frigate class they have proven to be easy prey for bigger ships and many folk skip them entirely or consign them to the ignominious role of salvager/loot gatherer, choosing other ships to do the actual fighting.
Many folk skip the destroyer, but not me.
I have recently started doing level 2 missions. Apparently these are balanced for cruiser class vessels but I have not yet trained cruisers so I am using a Thrasher destroyer and having a lot of fun. The blobs of enemies in these missions have enough DPS to chew up a destroyer very quickly. There are even some nasties with warp scramblers and webbers to prevent you from running away when things get tough. In order to survive I prepare for the missions carefully looking up what to expect and adjusting my ship fit out and strategy accordingly.
Its going well so far and I have done about ten missions without losing a ship. I have yet to get the "Human Cattle" mission which is a notorious ship killer but I am looking forward to giving it a try. I know I could probably do these faster if I trained up a cruiser but I imagine it would probably be a lot less enjoyable. I know some folks do these level 2's in a Rifter frigate. Now that is living dangerously.
I vary the set up a bit depending on the mission but mainly I use the Thrasher as a passive shield tanked artillery boat. Picture of load out from the excellent Eve Fitting Tool (click to enlarge):
The key to using this set-up is to keep the afterburner on constantly and use superior speed to choose a distance which keeps you safe from much of the enemy damage while still allowing you to hit them. I use Eve-Survival to suss out the missions in conjunction with Eveinfo's npc ship guide. Eveinfo actually has its own terrific mission database but sadly it is quite out of date and you cannot always rely on it.
Having chosen an optimal range for fighting then choose an appropriate shield hardener to reduce the most prominent type of long range damage that will still get to you. The above fit-out is optimised for thermal damage and the 36 figure against sustained defence means that this rig can absorb 36 dps of pure thermal damage forever without the tank breaking.
The passive shield tank is a doddle to use. Capacitor regenerates (+3.1) faster than it drains (-2.9) so I never run out even with afterburner and shield hardener on all the time. A quirk of passive shield tanking is that maximum shield regeneration occurs at about 30% shield. As long as shields remain above this point you are in no danger. If shields ever fall below this point (say 25%) the the tank is broken and you must warp out.
Some of the missions have fast webbing/scramming interceptors (for example Intercept the saboteurs) . The trick here is to pull the interceptors away from their escorts before they get close enough to web you. Once the posse is far enough behind kill the interceptor and then pick off the others at leisure.
Perhaps the most difficult missions I have come across have large blobs of fighters armed with long range missiles (for example Damsel in Distress) . My sniping tactics don't work here because if I am close enough to hit them they can hit me. I have had success with two approaches: The safe way is to snipe them one at a time watching my tank and warping out when my shield gets below 25%. Once the shield has recovered I go back in and finish them off. A riskier but faster approach is to swap the artillery for seven autocannons and a rocket launcher. I close in on the enemy and use these high dps close range weapons to kill them quickly before they can whittle down my tank.
More info on shield tanking, both passive and active can be found here and here. Your own skills will affect what you can fit and how it performs of course so ultimately you need to play around with EFT yourself to see what you can achieve. My own few words of advice for using EFT are to try and maximise the sustained defence rating (sustainable DPS) while ensuring that your capacitor recharge is still higher than its drain. Also be sure to right click on the defence panel and set the expected damage profile. The default profile assumes uniform damage distribution across all damage types which is virtually never the case in practise. Having a high effective hit points figure can also be a useful cushion of comfort if ever the expected DPS exceeds the sustained capability of your tank.
I have become a bit of a fan of passive shield tanking. Critics might point out that you can achieve a much higher temporary defence with active shield tanking. For as along as your capacitor lasts that is. One way of looking at active shield tanking is that you are turning capacitor energy into shield at a conversion rate of approximately 1:1. For the a Thrasher with just over 500 points of capacitor energy that would give me about an additional 500 point of shield boost but passive tanking gives me more than that from a single shield extender plus higher sustained defence to boot.