Some of the comments here are dated. With the 1.5 errata it was decided to "nerf" Cosmo and limit this card to encounter deck and player deck, so Doctor Strange can't benefit from this card regarding the invocation deck:

" Cosmo (Star-Lord, 20/Nebula, 20) was originally written to allow him to interact with any deck in the game. Many players have found him an invaluable companion for Doctor Strange and his invocation deck. However, we have found over time that this flexibility creates obstacles when we are trying to design scenarios or heroes who have a special deck that would be negatively affected by Cosmo’s ability. For that reason, we have decided to restrict Cosmo’s ability to only affecting player decks and the encounter deck, which still provides him a great deal of flexibility without standing in the way of new designs "

Great card and at a great cost! It allows you to choose any deck and discard the top card which can mitigate the luck factor quite a bit! expert troll strategy: you can mill the deck of your partner

Better than it seems at first glance.

If you can see what's in the top of a deck (Star-Lord, Jessica Drew, Heimdall...) You can ensure that he won't take any consequential damage.

Also... not 100% sure if that works, but if it does... just put him an Enraged in a Spider Woman deck and enjoy 3 attack without consequential damage.

I am confused by the phrasing "the deck". This doesn't tell me which deck it refers to. Is it the encounter deck, is it the player deck, or is it up to choice? filler, filler, filler, filler, filler, filler, filler, filler, filler, filler, filler, filler, filler, filler,

Should read: “Interrupt: When Cosmo attacks or thwarts, name a card type, then discard the top card of a player deck or the encounter deck. If that card is of the named type, Cosmo does not take consequential damage for this use.” (Changed “a deck” to “a player deck or the encounter deck”. Removed reminder text.)

Errata text on 1.6 rules reference

This is my all-time favorite ally. Cheap for blocks in certain builds, but that's only a small part of it.

With the right teammates and strategy, you can make a ridiculously strong combination with Cosmo. As an example, Cosmo is in Spider-Woman's deck and gets played. Spider-Woman gives Cosmo an Honorary Avenger. If you really wanted to go all out, an X-Man ally, specifically Storm (For reasons I'll explain later) could play Honorary X-Men on Cosmo. Now Cosmo has the tags for Guardian, Avenger, and X-Man. Here's where the fun begins:

Depending on what aspects you choose as Spider Woman, (Or if you play as Adam Warlock with an Avenger/X-men teammate) You can now play upgrades and supports for Cosmo until she is insanely powerful and to your liking. Including but not limited to:

Leadership: Laser Blaster (Guardian) Danger Room Training (X-men) Sky Cycle (Avenger) - This one is extra important since we can give Cosmo more than one activation per turn. Comms Implant (Guardian) Power Gloves (Avenger) Inspired Team Training

Aggression: Boot Camp Energy Spear (Guardian) Enraged - This Upgrade will have no downside if you are using one of a few select strategies to prevent Cosmo from taking any consequential damage

Protection: Protective Training (X-men)

Basic:
Sidearm C.I.T.T - Another really important one if you intend on using Cosmo more than once/twice per round.

Clearly Leadership and Aggression are the more important ones.

Now that you have Cosmo upgraded, you need a strategy to prevent her from taking Consequential damage, and there's quite a few. If you or a teammate is playing Doctor Strange, your Invocation Deck is made up of 100% Event cards. If your X-Men ally is playing Storm, her Environment deck will also work. If you are solo, or dont have either of the other options, Spider Woman's alter Ego action to prevent consequential damage once per round. After that, you will be relying on Cosmo's buffed hp, and cards like First Aid Med Team to heal her up between activations. Using cards like Shake it Off or Ready for Action to give Cosmo tough will also prevent some consequential damage depending on the aspects you've chosen (Your teammates can fill the other aspect roles if they so desire).

If all is setup, Cosmo can activate 2-4 times per turn, dealing a bunch of overkill and piercing damage and taking no consequential damage in return. Depending on the scenario, Cosmo can also thwart for quite a bit depending on upgrades.

P.S.

So far, the most ideal way to set this up is for a Spider Woman player to team up with a Storm player. Spider woman will play Aggression and Leadership with an Honorary Avenger, and Storm will play Protection with an Honorary X-men. Every time Cosmo activates, just choose the "Support" card type, and discard the top of Storm's weather deck. You're guaranteed to be correct, and Cosmo will take no damage.