At this point the basics of Eira’s mechanics have been thoroughly covered, so this is just a list of tips and details that some of the general guides may have glossed over.
Weave: You may want to keep this at rank B to avoid unlocking the additional attack. The additional attack makes it inconvenient to chain Weave into Mana Munitions, since you will need to move slightly to cancel the chain into Weave’s additional attack first.
Portal Leap: This should be abused to chain your smash combos. You should not run out of MP unless you are missing a significant number of smash hits and aren’t using Mana Phase.
Chaos Warp: This skill’s main benefits over Portal Leap are that it can be used to dodge red attacks and can travel a farther distance at a lower relative cost, since long Portal leaps are not efficient with MP. But in general, you should aim to maintain a close distance from enemies so that short Portal Leaps are sufficient to stay within range and Chaos Warp is not required. Chaos Warp should primarily be used only to dodge red attacks.
Bullet Storm > Bullet Rain > Bullet Hail: This is combo is 2+3+4 hits, with the attacks of each successive part of the combo having a lower multiplier than the previous. This is your bread and butter, because despite the longer animations this has higher DPS than WS > WB and DS > DB.
Warp Shot > Warp Blast: This combo is good for attacking while hugging or advancing toward an enemy if you don’t have the time for a full BS > BR > BH combo or if you feel you won’t be able to land most of that combo’s 9 hits.
Disruptor Shot > Disruptor Blast: Like WS > WB, this is good if you don’t have the time for a full BS > BR > BH combo or if you feel you won’t be able to land most of that combo’s 9 hits. But instead of advancing toward an enemy, this can put some distance between yourself and the enemy, which can be useful for setting up Mana Munitions and Infinity Shot.
Phase Burst: This gets a bad rap because it’s easy to miss some or all of the hits, but of the active skills that do damage this does the most damage per SP against a single target by far. The short animation also makes it safer than Infinity Shot and Quantum Ruin in many cases. Has a slight conical shape, so you'll miss some or all of hits if you're not close enough to a smaller boss. Unlike Infinity Shot and Quantum Ruin, Phase Burst cannot hit multiple targets simultaneously.
Infinity Shot: Has higher damage than Phase Burst but not proportional to the higher SP cost. This skill is easily interrupted, and the final explosion is also likely to miss if you are hugging a small boss.
Quantum Ruin: Has higher damage than Infinity Shot but not proportional to the higher SP cost.
Inverse Shot: This skill is pretty situational, because in terms of DPS it’s not efficient unless you need the distance it provides to use other skills. Primarily you’ll want to use this if you’re already in the middle of a BS > BR > BH or WS > WB combo and you need to create distance. The additional attack may be useful if you the enemy backs away out of your range as you perform Inverse Shot.
Entropic Rounds: Since this is a temporary damage buff, you’ll get the most mileage out of it by using it in conjunction with attack speed buffs (e.g., Werewolf Paw) and Gravity Rounds/Phase Burst/Infinity Shot/Quantum Ruin. However, if those skills are on cooldown, it may not make sense to wait for them before using Entropic Rounds.
Gravity Rounds: This should be used as soon as it’s off cooldown if the enemy is stationary.
Flux Rounds: This skill should only be necessary to generate MP if you’re consistently missing smashes and not using Mana Phase.
Mana Phase: Particularly useful for recovering stamina and MP at higher attack speeds, since you’re more likely to have surplus SP while your active skills are on cooldown and more likely to run out of stamina.
If you’re low on MP despite Mana Phase and Flux Rounds, or if you want to save up MP for some reason, you can avoid the long recovery animation of Bullet Hail by following with Inverse Shot and canceling Inverse Shot’s recovery animation by quickly tapping right click (Mana Munitions).